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

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+201x^88+16x^89+160x^90+368x^91+560x^92+368x^93+160x^94+16x^95+194x^96+3x^104+1x^176

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 3.66 seconds.