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

generates a code of length 93 over Z2[X]/(X^4) who´s minimum homogenous weight is 87.

Homogenous weight enumerator: w(x)=1x^0+84x^87+248x^88+248x^89+452x^90+350x^91+591x^92+360x^93+548x^94+334x^95+337x^96+180x^97+116x^98+54x^99+101x^100+36x^101+20x^102+10x^103+16x^104+8x^105+1x^112+1x^152

The gray image is a linear code over GF(2) with n=744, k=12 and d=348.
This code was found by Heurico 1.16 in 1.55 seconds.