The generator matrix

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

generates a code of length 65 over Z2[X]/(X^2) who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+64x^55+110x^56+148x^57+227x^58+250x^59+240x^60+260x^61+238x^62+244x^63+239x^64+212x^65+241x^66+242x^67+200x^68+210x^69+237x^70+138x^71+149x^72+142x^73+92x^74+72x^75+44x^76+50x^77+21x^78+10x^79+8x^80+2x^81+4x^83+1x^88

The gray image is a linear code over GF(2) with n=130, k=12 and d=55.
This code was found by Heurico 1.10 in 0.813 seconds.