The generator matrix

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

generates a code of length 98 over Z2[X]/(X^4) who´s minimum homogenous weight is 94.

Homogenous weight enumerator: w(x)=1x^0+236x^94+700x^95+660x^96+658x^97+382x^98+368x^99+296x^100+214x^101+170x^102+116x^103+65x^104+100x^105+56x^106+52x^107+16x^108+2x^110+1x^112+1x^114+1x^116+1x^118

The gray image is a linear code over GF(2) with n=784, k=12 and d=376.
This code was found by Heurico 1.16 in 0.672 seconds.