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

generates a code of length 67 over Z2[X]/(X^2) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+92x^54+114x^55+232x^56+340x^57+421x^58+534x^59+665x^60+774x^61+719x^62+822x^63+920x^64+1038x^65+1009x^66+1018x^67+1026x^68+1008x^69+1013x^70+880x^71+773x^72+672x^73+604x^74+496x^75+392x^76+290x^77+210x^78+152x^79+78x^80+38x^81+25x^82+16x^83+9x^84+2x^86+1x^114

The gray image is a linear code over GF(2) with n=134, k=14 and d=54.
This code was found by Heurico 1.10 in 11.9 seconds.