The generator matrix

 1  0  0  0  1  1  1  0  1 X^2  1  1  X  0  1  X  1  1  0  1 X^2  1  1  1 X^2  1  0 X^2+X  1  X X^2  1  X X^2+X X^2  1  0  1  1 X^2  1  X  1  1  1  0  1  1  0  0 X^2+X X^2+X  1  1  0  1  1  1  1  1  X  1  1 X^2+X  X  1  X X^2  1  X X^2+X  1  0  X X^2 X^2  1 X^2  1
 0  1  0  0  1 X^2  1  1 X^2+1  1 X^2 X^2  1  X X^2+X+1  1 X^2+X X+1  1 X^2+X+1  1  X X+1 X^2+X+1 X^2+X X^2  1 X^2+X  0  X  0  1  1  X  1 X^2+X  1 X^2+1  X X^2  X  1  1 X^2+X+1 X^2+X  1 X^2 X^2+1  X  1 X^2  1 X+1 X^2+X+1  1 X+1  X X^2 X^2+X X^2 X^2+X X^2+1  1 X^2  1  0  1  1 X^2+X+1 X^2+X  0  1  1  1  1  1 X^2+X  1  X
 0  0  1  0  X  0 X^2+X  X  1  1 X^2+X+1  1  1  1 X+1 X^2+X X^2+X  1  0  X X+1  0  0 X^2+1  X X^2+1  1  1 X^2+X+1 X^2  1 X+1  X  1 X^2+1 X+1 X+1 X^2 X^2  1 X^2+1 X^2+X X+1  0 X^2 X^2+1 X^2+X  1  1 X^2+X+1  1  0 X^2+1 X+1  0 X^2 X^2+X+1 X^2+X+1 X^2+X  X  1 X^2+1 X^2+1  1  1 X+1 X^2+X X^2+X+1 X^2+1  X  X X^2 X^2 X^2+1  X X^2+X+1 X^2+X X^2+X  1
 0  0  0  1  X  1 X+1 X+1 X+1 X^2+X+1 X^2 X^2+1 X^2+X X^2+X+1 X^2+X  X  0  X X^2+X+1 X^2  0 X^2+1 X^2+1 X+1  1 X^2+X  1 X^2+X X^2+1  1  1 X^2+1 X+1 X^2 X^2+X  1 X+1 X^2+X  0  X  X  0 X^2+X  X X+1 X^2 X^2+X X+1 X^2+1  1 X^2+X  0  X X^2+1  X X^2 X+1  0 X^2+X X+1 X+1  0  X X^2+1 X^2  X  X  0 X^2  1  1 X^2+X+1 X+1  1  0  1  0  X X^2
 0  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2  0  0  0  0 X^2  0 X^2  0 X^2  0  0 X^2 X^2 X^2  0  0  0 X^2  0 X^2  0  0  0 X^2 X^2  0  0  0  0  0 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2  0  0  0  0 X^2 X^2 X^2  0  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+482x^72+1126x^74+1387x^76+1456x^78+1256x^80+936x^82+681x^84+458x^86+288x^88+86x^90+28x^92+2x^94+4x^96+1x^104

The gray image is a linear code over GF(2) with n=316, k=13 and d=144.
This code was found by Heurico 1.11 in 53.5 seconds.