The generator matrix

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

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+138x^87+449x^88+476x^89+336x^90+450x^91+543x^92+418x^93+286x^94+418x^95+365x^96+124x^97+44x^98+8x^99+14x^100+6x^101+6x^102+2x^103+1x^104+4x^107+2x^111+2x^115+2x^116+1x^124

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 1.08 seconds.