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

generates a code of length 79 over Z2[X]/(X^4) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+396x^74+64x^75+553x^76+256x^77+660x^78+368x^79+634x^80+288x^81+420x^82+48x^83+258x^84+116x^86+20x^88+8x^90+5x^92+1x^128

The gray image is a linear code over GF(2) with n=632, k=12 and d=296.
This code was found by Heurico 1.16 in 95.1 seconds.