The generator matrix

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

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+156x^93+445x^94+426x^95+512x^96+320x^97+463x^98+422x^99+443x^100+288x^101+367x^102+156x^103+58x^104+10x^105+5x^106+2x^107+6x^108+2x^109+2x^111+2x^116+2x^117+6x^121+1x^128+1x^132

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 26.2 seconds.