The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X^2 1 1 1 1 X 1 1 1 1 X 1 1 1 X 1 X 1 1 1 X 1 1 1 X 1 X^2 0 1 1 0 0 1 1 1 1 1
0 X 0 0 0 X^2 0 X^2 0 X X X^2+X X X^2+X X^2+X X X^2 X X^2 0 0 X X X^2+X 0 X X X^2 0 X^2+X X^2+X X^2 X 0 X^2+X 0 0 X^2+X X X^2 X X 0 X^2 X X^2 X X^2+X 0 X^2 X^2 X X^2+X X X^2 0 0 X^2+X X^2 0 X X^2 X X 0 X X^2+X X^2 X X^2+X X^2 0 X X^2 0 X X^2 X X^2+X 0 0 X X X^2+X X^2 X^2+X X^2
0 0 X 0 0 X^2 X X X X^2+X X X^2 X X^2+X 0 0 0 X X^2+X X^2+X X^2 0 X^2+X X^2 X^2+X X^2+X 0 X^2 X^2+X 0 X^2+X 0 X^2+X X^2 X^2+X X^2+X 0 0 X^2 X^2+X X^2+X X^2 X 0 X^2 0 X^2+X X X X^2+X X X^2 0 X^2 X^2 X X X^2 X^2+X 0 X^2 X 0 0 X X^2 X^2+X 0 0 X^2 X X X 0 X^2+X X^2 X X X^2+X X X X 0 0 0 X^2 X
0 0 0 X 0 X X X^2+X X^2 0 X X 0 X^2+X X X^2 X^2+X X^2+X 0 0 X^2 X^2+X X^2 X X X^2+X 0 0 X 0 X^2 X^2+X X^2 X X^2+X X^2+X X^2 0 0 X X X X^2 0 X X X X^2 X^2 X^2+X 0 0 X X^2 X^2+X X 0 X^2 0 X^2 X 0 0 X 0 X^2 X^2+X X^2+X X^2 X^2+X X^2 0 0 X^2 X^2+X X^2+X X^2 X^2 0 X^2+X X^2 0 X X^2+X 0 X 0
0 0 0 0 X X X^2 X X^2+X X X 0 0 X^2 X X 0 X X^2+X 0 X^2+X X^2 0 X^2+X X^2 0 X^2 0 X^2+X X X^2+X X^2+X X^2 X^2+X X^2+X X X^2+X 0 X^2+X X^2 X^2 X X 0 0 X^2 0 X X^2 X X X X^2 0 X^2+X 0 X^2 X^2 0 0 X^2 X^2 X^2+X X X X^2+X X^2 X X^2 0 0 X^2+X X^2+X X 0 X X X 0 X^2 X^2 X^2 X^2 0 X X X
generates a code of length 87 over Z2[X]/(X^3) who´s minimum homogenous weight is 80.
Homogenous weight enumerator: w(x)=1x^0+226x^80+16x^82+476x^84+304x^86+531x^88+160x^90+192x^92+105x^96+28x^100+8x^104+1x^152
The gray image is a linear code over GF(2) with n=348, k=11 and d=160.
This code was found by Heurico 1.16 in 34.9 seconds.