The generator matrix

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

generates a code of length 78 over Z2[X]/(X^2) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+25x^64+102x^65+216x^66+320x^67+394x^68+502x^69+549x^70+658x^71+691x^72+754x^73+878x^74+858x^75+844x^76+900x^77+994x^78+922x^79+905x^80+880x^81+868x^82+814x^83+690x^84+662x^85+501x^86+358x^87+344x^88+242x^89+186x^90+150x^91+72x^92+48x^93+28x^94+14x^95+1x^96+6x^97+4x^98+2x^99+1x^120

The gray image is a linear code over GF(2) with n=156, k=14 and d=64.
This code was found by Heurico 1.10 in 14.3 seconds.