The generator matrix

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

generates a code of length 66 over Z2[X]/(X^2) who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+118x^55+174x^56+236x^57+326x^58+330x^59+424x^60+420x^61+424x^62+446x^63+519x^64+502x^65+455x^66+532x^67+447x^68+458x^69+470x^70+404x^71+372x^72+298x^73+240x^74+180x^75+144x^76+122x^77+57x^78+32x^79+30x^80+12x^81+11x^82+6x^83+1x^84+1x^94

The gray image is a linear code over GF(2) with n=132, k=13 and d=55.
This code was found by Heurico 1.10 in 57.1 seconds.