The generator matrix

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

generates a code of length 79 over Z2[X]/(X^2) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+200x^66+643x^68+1038x^70+1227x^72+1532x^74+1759x^76+1838x^78+1838x^80+1734x^82+1611x^84+1210x^86+814x^88+528x^90+265x^92+106x^94+31x^96+6x^98+2x^100+1x^120

The gray image is a linear code over GF(2) with n=158, k=14 and d=66.
This code was found by Heurico 1.10 in 14.8 seconds.