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  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 X^3  1 X^3+X^2  0  X  1
 0  X  0  X X^3 X^3 X^3+X X^3+X X^2 X^2+X X^2 X^2+X X^3+X^2 X^3+X^2+X X^3+X^2 X^3+X^2+X  0  X X^3 X^2+X X^2 X^2+X  X  0 X^2 X^3+X^2+X X^3 X^3+X X^2 X^3+X X^2 X^3+X^2+X  0 X^3+X^2 X^2+X  X X^3+X^2  0 X^2+X  X X^2+X X^3 X^2  X X^2+X  0 X^3+X^2  X X^3+X^2 X^3+X^2  X X^3+X^2+X  0 X^2+X X^3+X^2+X X^3+X^2  0  X X^3+X X^2+X X^2 X^3+X X^3  0 X^3+X^2  0 X^3 X^3+X^2 X^2+X X^3+X^2+X  X X^3 X^3+X^2+X X^3+X^2 X^3+X^2+X X^3 X^3+X X^3+X^2+X X^3+X^2+X  0 X^3+X^2 X^3 X^3+X  X X^2+X  0  X X^3+X X^3  X  X X^3+X
 0  0  X  X X^2 X^3+X^2+X X^2+X X^3+X^2 X^2 X^2+X  X  0  0  X X^3+X^2+X X^3+X^2  0  X X^3+X^2+X X^3+X^2 X^2+X X^3 X^3+X^2+X X^2 X^3+X^2 X^2+X X^3+X X^2  X  0 X^3 X^3+X X^3 X^3+X X^2+X X^2 X^2 X^3+X  X X^3 X^3 X^2+X  0 X^2+X X^2 X^3+X^2 X^2+X X^3+X X^2+X  0  0 X^3+X^2+X X^3+X^2+X X^3+X X^3 X^2 X^3+X X^3+X X^3+X^2 X^2 X^3+X X^3+X^2+X  0 X^2 X^3+X X^3+X^2 X^3  X X^3+X^2+X X^2 X^3+X^2 X^3+X X^3+X^2+X X^3+X^2+X X^3 X^2 X^3  X X^3+X X^3+X^2+X X^3 X^2+X X^2+X X^2+X  0 X^3+X X^2  X  X X^3+X^2+X X^3+X X^3+X
 0  0  0 X^3 X^3 X^3  0 X^3  0 X^3 X^3 X^3 X^3  0  0  0 X^3  0  0 X^3 X^3  0 X^3  0 X^3  0 X^3  0  0 X^3  0 X^3 X^3  0  0 X^3  0 X^3 X^3  0 X^3  0 X^3 X^3  0  0 X^3  0  0  0 X^3 X^3 X^3  0  0 X^3  0 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3  0  0 X^3 X^3  0  0  0 X^3 X^3  0  0 X^3  0  0 X^3 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3 X^3 X^3

generates a code of length 92 over Z2[X]/(X^4) who´s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+127x^88+106x^89+279x^90+228x^91+635x^92+204x^93+233x^94+88x^95+92x^96+10x^97+39x^98+4x^99+1x^100+1x^174

The gray image is a linear code over GF(2) with n=736, k=11 and d=352.
This code was found by Heurico 1.16 in 1.02 seconds.