The generator matrix

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

generates a code of length 79 over Z2[X]/(X^3) who´s minimum homogenous weight is 73.

Homogenous weight enumerator: w(x)=1x^0+216x^73+287x^74+466x^75+413x^76+406x^77+345x^78+364x^79+269x^80+296x^81+165x^82+238x^83+117x^84+164x^85+97x^86+96x^87+42x^88+16x^89+29x^90+36x^91+20x^92+6x^93+4x^94+2x^96+1x^98

The gray image is a linear code over GF(2) with n=316, k=12 and d=146.
This code was found by Heurico 1.11 in 0.422 seconds.