The generator matrix

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

generates a code of length 98 over Z2[X]/(X^4) who´s minimum homogenous weight is 93.

Homogenous weight enumerator: w(x)=1x^0+70x^93+455x^94+492x^95+600x^96+342x^97+514x^98+284x^99+396x^100+336x^101+347x^102+98x^103+80x^104+18x^105+12x^106+12x^107+16x^108+2x^109+10x^111+8x^112+1x^116+1x^132+1x^136

The gray image is a linear code over GF(2) with n=784, k=12 and d=372.
This code was found by Heurico 1.16 in 1.45 seconds.