The generator matrix

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

generates a code of length 77 over Z2[X]/(X^2) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+196x^64+626x^66+953x^68+1330x^70+1504x^72+1676x^74+1954x^76+1864x^78+1714x^80+1602x^82+1255x^84+832x^86+539x^88+246x^90+70x^92+14x^94+5x^96+2x^98+1x^136

The gray image is a linear code over GF(2) with n=154, k=14 and d=64.
This code was found by Heurico 1.10 in 14.4 seconds.