The generator matrix

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

generates a code of length 79 over Z2[X]/(X^3) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+205x^72+92x^73+408x^74+172x^75+484x^76+172x^77+534x^78+164x^79+507x^80+164x^81+380x^82+164x^83+280x^84+84x^85+144x^86+12x^87+61x^88+30x^90+17x^92+6x^94+7x^96+2x^98+3x^100+3x^104

The gray image is a linear code over GF(2) with n=316, k=12 and d=144.
This code was found by Heurico 1.16 in 1.59 seconds.