The generator matrix

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

generates a code of length 64 over Z2[X]/(X^2) who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+50x^51+120x^52+212x^53+333x^54+418x^55+532x^56+644x^57+689x^58+776x^59+889x^60+954x^61+999x^62+1060x^63+1050x^64+1004x^65+1005x^66+1044x^67+891x^68+792x^69+766x^70+580x^71+494x^72+352x^73+270x^74+190x^75+112x^76+66x^77+34x^78+38x^79+6x^80+8x^81+4x^83+1x^104

The gray image is a linear code over GF(2) with n=128, k=14 and d=51.
This code was found by an older version of Heurico in 0 seconds.