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  0  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1 X^2  1  1  1  1  1  1  1  X  0  1  1  0  1 X^2  1  0  1  X  1  1  1  0  X  X  1  0 X^2  X
 0  X  0  0  0 X^2  0 X^2  0  X  X  X X^2+X X^2+X  X  X X^2 X^2 X^2+X X^2 X^2+X  X X^2+X  0  0  X  0 X^2+X X^2 X^2+X X^2+X X^2 X^2 X^2+X  X X^2  X  X X^2 X^2+X X^2+X  0 X^2+X X^2+X  0 X^2+X X^2+X X^2+X X^2+X  0  X  0 X^2+X  0  X  0  X X^2+X  0 X^2  X  X  X X^2+X  X  0  X X^2  0 X^2 X^2 X^2  X  X  0  X  X  X  0
 0  0  X  0  0 X^2  X  X  X X^2+X  X X^2 X^2+X  X X^2 X^2 X^2+X  X  0  X  0  0  X  0 X^2+X X^2  0 X^2+X  0  X X^2+X X^2  X  0  0  0 X^2+X X^2+X  X X^2  X X^2  X X^2 X^2+X X^2 X^2+X X^2+X X^2  0  0 X^2 X^2 X^2+X X^2+X X^2+X X^2 X^2  X  X X^2+X  0  X  0 X^2+X  0  X X^2+X X^2  0 X^2 X^2+X  X X^2 X^2+X  0  0 X^2 X^2
 0  0  0  X  0  X  X X^2+X X^2  0  0 X^2+X  X  X  X X^2  X  0 X^2 X^2+X  X X^2 X^2  X X^2  X X^2 X^2+X  X  0  X  0  0 X^2+X X^2+X  0 X^2+X X^2 X^2+X  0  X  0 X^2  0 X^2+X  X X^2+X  X  0 X^2+X X^2+X X^2+X  X X^2 X^2  X  X X^2  X  X X^2+X  X  X  0 X^2+X X^2+X  X X^2+X  0 X^2+X  X  X  0 X^2  X X^2+X X^2+X X^2 X^2
 0  0  0  0  X  X X^2  X X^2+X  X  0 X^2+X  X  0 X^2  X X^2+X  X  X X^2  0 X^2  0  X  0 X^2+X  X  0 X^2 X^2+X X^2+X X^2  0  0  X  0 X^2 X^2  0  X  X  X X^2+X X^2 X^2+X X^2+X X^2 X^2  0 X^2+X  0 X^2  0  X X^2+X  X  0 X^2+X  0 X^2+X X^2+X X^2+X X^2  0  X X^2 X^2+X X^2+X  X  X X^2+X  X X^2+X X^2+X X^2+X  X X^2+X  0 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+135x^72+234x^74+349x^76+382x^78+386x^80+204x^82+172x^84+64x^86+61x^88+34x^90+15x^92+10x^94+1x^128

The gray image is a linear code over GF(2) with n=316, k=11 and d=144.
This code was found by Heurico 1.16 in 0.646 seconds.