The generator matrix

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

generates a code of length 92 over Z2[X]/(X^4) who´s minimum homogenous weight is 87.

Homogenous weight enumerator: w(x)=1x^0+200x^87+267x^88+554x^89+323x^90+676x^91+285x^92+548x^93+281x^94+488x^95+196x^96+136x^97+33x^98+72x^99+18x^100+8x^101+4x^103+2x^105+2x^110+1x^132+1x^134

The gray image is a linear code over GF(2) with n=736, k=12 and d=348.
This code was found by Heurico 1.16 in 1.22 seconds.