The generator matrix

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

generates a code of length 66 over Z2[X]/(X^2) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+44x^54+100x^55+181x^56+218x^57+272x^58+352x^59+408x^60+432x^61+418x^62+466x^63+503x^64+478x^65+500x^66+504x^67+484x^68+518x^69+417x^70+410x^71+365x^72+292x^73+242x^74+170x^75+148x^76+98x^77+80x^78+40x^79+22x^80+12x^81+10x^82+6x^83+1x^102

The gray image is a linear code over GF(2) with n=132, k=13 and d=54.
This code was found by an older version of Heurico in 0 seconds.