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 X^3  1  1  1  1  1  1  1  1  1  1  1  1  X  1 X^3  1 X^3+X^2  1  1  X X^2  1  X  1  X X^2  1  X  1  1  1  X  1 X^2 X^3+X^2  1  1  X X^3 X^2 X^2  1  1  0  1
 0  X  0  X X^3  0 X^2+X X^3+X^2+X  0 X^3  X X^3+X X^3 X^2+X X^3 X^2+X X^2 X^3+X X^3+X^2 X^3+X^2+X  X X^2 X^2 X^2+X X^3+X^2+X X^3+X^2 X^3+X^2 X^3+X X^3+X^2 X^2 X^2+X  X  0 X^3 X^3+X^2+X X^3+X^2+X X^2 X^3+X X^3+X X^3+X^2 X^3+X^2+X X^2  0 X^3+X X^3+X X^3+X^2 X^3+X X^3 X^3+X X^2 X^2+X  X X^3  X X^3+X^2+X X^3 X^3+X^2+X X^3 X^3+X^2+X X^3+X X^2 X^3 X^3+X^2+X X^2 X^2 X^2 X^2+X X^2+X  X X^3+X  X X^3 X^3+X^2  X  X X^3+X X^3 X^3 X^3+X^2 X^2  X X^3+X  0 X^3+X^2+X X^3+X X^3+X^2 X^2+X  X  X X^2+X X^2+X  X  X  X  X X^3+X^2+X X^3+X^2+X  X  0
 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^3+X^2 X^3+X^2  X X^3+X X^3+X^2 X^2 X^3+X^2+X X^2+X X^2 X^3 X^3+X X^2 X^3+X^2+X X^3+X^2+X  0 X^2+X  0  0  X X^3+X^2 X^3+X^2+X X^2+X X^3+X^2+X  X  0 X^2 X^2  X X^3+X^2  X  0 X^3+X X^2  X X^3 X^2  X X^3  X X^3+X X^3+X  0 X^3+X^2  0 X^2  0 X^3 X^3+X^2+X 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 X^2 X^2 X^3 X^3+X^2  0 X^3+X^2+X X^2 X^2 X^2+X X^3+X X^3+X^2+X X^3+X^2+X  X  X X^2  X X^3+X^2 X^3+X^2+X X^3+X X^3+X^2+X X^3 X^3 X^3+X X^2  0 X^2 X^2 X^2 X^3+X X^3 X^3+X X^2  0
 0  0  0 X^2 X^2 X^3+X^2  0 X^3+X^2 X^2 X^3 X^2 X^3  0  0 X^2 X^2  0  0 X^3  0 X^2 X^2 X^2 X^2 X^3+X^2 X^3+X^2 X^2 X^3+X^2  0  0 X^3 X^3  0 X^2 X^3+X^2  0 X^3+X^2 X^3+X^2  0 X^3 X^2 X^2 X^3  0 X^3 X^3 X^2 X^3+X^2 X^3 X^3 X^3 X^3+X^2 X^3+X^2 X^3 X^2 X^3 X^3 X^3 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2  0 X^3+X^2  0 X^2  0 X^2 X^2 X^3 X^3+X^2  0 X^3 X^3+X^2  0 X^3  0 X^3+X^2 X^3+X^2 X^3 X^3 X^3  0 X^3+X^2 X^3+X^2 X^2 X^3+X^2 X^3+X^2 X^3 X^3 X^3+X^2 X^2  0  0 X^2 X^2 X^3+X^2  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+98x^93+238x^94+314x^95+373x^96+386x^97+473x^98+514x^99+465x^100+400x^101+298x^102+178x^103+57x^104+102x^105+87x^106+34x^107+31x^108+22x^109+14x^110+9x^112+1x^114+1x^162

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.