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

generates a code of length 98 over Z2[X]/(X^4) who´s minimum homogenous weight is 92.

Homogenous weight enumerator: w(x)=1x^0+123x^92+178x^93+279x^94+330x^95+399x^96+610x^97+431x^98+628x^99+304x^100+242x^101+227x^102+122x^103+75x^104+42x^105+51x^106+20x^107+25x^108+2x^110+4x^111+2x^114+1x^168

The gray image is a linear code over GF(2) with n=784, k=12 and d=368.
This code was found by Heurico 1.16 in 1.61 seconds.