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

generates a code of length 99 over Z2[X]/(X^4) who´s minimum homogenous weight is 93.

Homogenous weight enumerator: w(x)=1x^0+118x^93+241x^94+192x^95+362x^96+332x^97+700x^98+328x^99+712x^100+282x^101+309x^102+136x^103+175x^104+108x^105+29x^106+24x^107+25x^108+4x^109+8x^111+4x^112+4x^113+1x^122+1x^172

The gray image is a linear code over GF(2) with n=792, k=12 and d=372.
This code was found by Heurico 1.16 in 1.67 seconds.