The generator matrix

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

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+47x^72+264x^73+230x^74+474x^75+318x^76+466x^77+272x^78+402x^79+208x^80+366x^81+165x^82+238x^83+133x^84+164x^85+85x^86+94x^87+46x^88+72x^89+11x^90+8x^91+13x^92+10x^93+3x^94+2x^96+2x^97+2x^98

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 1.18 seconds.