The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^3+X^2  1 X^3+X  1  1  1  0  1  1 X^2+X X^3+X^2  1  1  1  1 X^3+X  1  1  0  1  1 X^2+X  1  1 X^3+X^2  1 X^3+X  1  1  0  1 X^2+X  1  1  1  1 X^3+X^2  1  1 X^3+X  1  1  0  1 X^2+X  1  1  1 X^3  1  1 X^3+X^2+X  1  1  1 X^3+X^2 X^3+X^2  1 X^3+X X^3+X  1  1  1  1  0 X^3+X^2+X  1  1  1  1  1  1  1 X^2  X  1  1  1  1  1  1  1  1  1 X^3  1  1  1  1 X^2+X
 0  1 X+1 X^2+X X^2+1  1 X^3+X^2 X^3+X^2+X+1  1 X^3+X  1 X^3+1 X+1  0  1 X^2+X X^2+1  1  1 X^3+X^2 X^3+X^2+X+1 X^3+X X^3+1  1  0 X+1  1 X^2+X X^2+1  1 X^3+X^2 X^3+X^2+X+1  1 X^3+1  1 X^3+X X^3+X^2+X  1 X+1  1  0 X^2+1  X X^3+X^2+X+1  1 X^3+X^2 X^3+1  1  0 X+1  1 X^2+1  1 X^2+X X^3+X X^3+X+1  1 X^3 X^3+X^2+1  1  0 X+1 X^2+1  1  1 X^2+X  1  1 X^3+X^2 X^2 X^3+X^2+X+1 X^3+1  1  1 X^3+X X^3+X^2+X+1 X^3+X^2 X^3+1 X^3+X+1 X^3+X^2+1 X^3+X  1  1 X^3  X X^3+X^2+X  0 X^3 X+1 X^3+X+1 X^2+X  1  1 X^3+X  X X^2+X+1 X^2+X  1
 0  0 X^3  0  0  0  0  0  0  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0  0 X^3  0 X^3 X^3 X^3  0 X^3  0  0  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0 X^3  0  0 X^3  0 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3  0  0 X^3 X^3  0  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3
 0  0  0 X^3  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0  0  0 X^3  0  0  0 X^3  0  0 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0  0  0  0  0  0  0 X^3 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3  0  0  0  0 X^3 X^3 X^3  0  0 X^3 X^3  0  0  0 X^3 X^3  0 X^3  0  0 X^3 X^3 X^3  0  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3  0  0  0 X^3
 0  0  0  0 X^3  0  0 X^3  0  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3  0  0 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3  0 X^3  0  0  0  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3  0 X^3 X^3  0 X^3  0  0 X^3  0  0 X^3  0 X^3  0 X^3 X^3  0 X^3  0  0 X^3  0 X^3 X^3 X^3  0 X^3  0  0  0  0 X^3 X^3 X^3 X^3  0 X^3  0 X^3  0  0  0 X^3 X^3 X^3  0  0
 0  0  0  0  0 X^3 X^3 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0 X^3  0  0  0  0 X^3 X^3 X^3 X^3  0 X^3  0 X^3  0  0 X^3  0  0 X^3 X^3  0  0  0 X^3  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3  0  0 X^3 X^3  0  0  0 X^3 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0  0  0  0  0  0 X^3 X^3  0  0 X^3  0 X^3 X^3 X^3  0  0 X^3  0 X^3 X^3  0 X^3 X^3  0  0  0 X^3  0  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+200x^93+429x^94+600x^95+242x^96+352x^97+455x^98+352x^99+230x^100+600x^101+427x^102+200x^103+4x^104+1x^106+1x^124+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 47.7 seconds.