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

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+116x^87+193x^88+336x^89+272x^90+476x^91+469x^92+560x^93+432x^94+424x^95+267x^96+212x^97+84x^98+116x^99+46x^100+40x^101+8x^102+12x^103+10x^104+4x^105+4x^106+8x^107+5x^108+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 1.38 seconds.