The generator matrix

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

generates a code of length 92 over Z2[X]/(X^4) who´s minimum homogenous weight is 87.

Homogenous weight enumerator: w(x)=1x^0+112x^87+638x^88+496x^89+32x^90+288x^91+960x^92+288x^93+32x^94+496x^95+638x^96+112x^97+2x^120+1x^128

The gray image is a linear code over GF(2) with n=736, k=12 and d=348.
This code was found by Heurico 1.16 in 0.891 seconds.