The generator matrix

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

generates a code of length 63 over Z2[X]/(X^2) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+46x^53+109x^54+170x^55+224x^56+234x^57+246x^58+234x^59+211x^60+268x^61+266x^62+256x^63+216x^64+208x^65+271x^66+216x^67+203x^68+174x^69+132x^70+106x^71+87x^72+78x^73+55x^74+38x^75+14x^76+16x^77+9x^78+4x^79+4x^80

The gray image is a linear code over GF(2) with n=126, k=12 and d=53.
This code was found by an older version of Heurico in 0 seconds.