The generator matrix

 1  0  0  0  0  1  1  1  X  1  1  0  1  X  0  1  1  1  X  1  0  1  1  1  1  1  X  X  X  1  X  1  0  0  1  X  1  0  1  X  X  1  0  0  1  1  0  0  1  1  1  1  1  0  0  0  X  X  X  0  1  0  0  X  1  1  X  0  X  1  0  X  1  1  1  1  0  1  0
 0  1  0  0  0  X  X  X  0 X+1  1  1 X+1  1  1 X+1 X+1  0  1  X  X  X  1 X+1  0 X+1  1  1  1  0  0 X+1  X  1  X  X  1  1  X  1  X  0  1  1  X  X  X  0  0  0  0  1  1  X  0  1  1  1  0  1  0  1  1  1  0  0  1  1  0  0  1  1  X  0  X  X  0  0  0
 0  0  1  0  0  0  0  0  0  0  0  X  X  X  0  X X+1  1  1  1  1 X+1 X+1 X+1  1  1 X+1 X+1  1  X  X X+1  1  0  X  0  1  1  1  1  1 X+1  X  0  0 X+1  1  1 X+1  X  0 X+1  1  1  1  X  1 X+1  1 X+1  1  X  0  X  X  X  0  1  1 X+1  X  0 X+1 X+1 X+1  1  1  1  0
 0  0  0  1  0  0 X+1  1  1  0  X  0  1 X+1 X+1 X+1 X+1  1  X  X X+1 X+1  0  1  X  X X+1  1  0  0  X  0  0  X  0  1  1  X X+1 X+1  0  0 X+1  X  1  X  1 X+1  1  X X+1  1 X+1  1  0  1  1 X+1  1 X+1  X  0 X+1  X X+1  1 X+1  X  X X+1  0  1  X  0  0  0  1 X+1  1
 0  0  0  0  1  1 X+1  0  1  X X+1 X+1  X  1  X X+1  1 X+1  X X+1  1  X X+1  0  X  0  0  1 X+1  1  1 X+1  0  1  X X+1  1  X  0  0  0  0  1  0  X  1  X X+1 X+1  X  0  0  1  0  1 X+1  0 X+1  X  X  0  X X+1 X+1  0 X+1  X X+1  1  X  0 X+1 X+1  1 X+1  X X+1 X+1  X

generates a code of length 79 over Z2[X]/(X^2) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+88x^72+206x^74+171x^76+146x^78+109x^80+80x^82+73x^84+30x^86+42x^88+24x^90+17x^92+24x^94+8x^96+2x^98+3x^100

The gray image is a linear code over GF(2) with n=158, k=10 and d=72.
This code was found by Heurico 1.16 in 0.245 seconds.