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

generates a code of length 92 over Z2[X]/(X^4) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+42x^86+284x^87+227x^88+410x^89+338x^90+512x^91+624x^92+532x^93+303x^94+280x^95+175x^96+166x^97+62x^98+68x^99+8x^100+44x^101+6x^102+8x^103+5x^104+1x^158

The gray image is a linear code over GF(2) with n=736, k=12 and d=344.
This code was found by Heurico 1.16 in 1.33 seconds.