The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  0  0  X X^2  1  1  X X^2  1  X  1 X^2  1  0  1  0  1 X^2  X  X  1  1  X  1  X  1
 0  X  0  0  0  0  0  0 X^2 X^2  X X^2+X  X  0  0 X^2 X^2+X X^2+X  X  X  X  X  0  X X^2+X  X  0  X X^2+X X^2 X^2+X X^2 X^2 X^2+X  X X^2+X  X  X X^2 X^2  X  0  X  0  X X^2+X X^2 X^2+X  X X^2  X X^2  X  X  X  X  X  0 X^2  X  0 X^2  0
 0  0  X  0  0  0  0  0  0  0  0  0 X^2 X^2+X X^2+X X^2+X  X X^2+X X^2+X  X X^2 X^2 X^2+X X^2+X  0  0  X  X  X X^2+X X^2+X X^2+X X^2 X^2 X^2+X X^2  X  X  X  0  X  X  0  X X^2+X X^2+X  X X^2  X X^2+X  X X^2  X X^2+X  0 X^2  X X^2  X X^2+X  0  0 X^2
 0  0  0  X  0  0 X^2 X^2+X  X  X  X  X X^2 X^2+X  X X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  X X^2+X  X X^2  X X^2+X X^2+X  X X^2+X  0 X^2  0  0 X^2+X  0  X X^2+X  0  0 X^2  X  X X^2  X X^2 X^2+X X^2  X X^2 X^2  0 X^2  0  X X^2+X X^2+X X^2+X X^2  X X^2
 0  0  0  0  X  0 X^2+X X^2+X  X X^2 X^2+X X^2+X  0  X  X  0 X^2  X  0 X^2+X X^2+X  X X^2+X  X X^2 X^2  X X^2 X^2  0 X^2+X X^2  0 X^2+X  X  0  0 X^2+X  X  0  0 X^2+X X^2  0  0  X  0 X^2  X  X  X  X X^2  X  X X^2+X  0 X^2 X^2+X  X  0 X^2 X^2+X
 0  0  0  0  0  X  X X^2 X^2+X  X X^2+X X^2  X  X  0  X  0 X^2+X X^2+X  0  X X^2 X^2 X^2+X X^2  X X^2+X X^2+X X^2  X X^2 X^2 X^2+X  0  X X^2  X  0  0 X^2 X^2 X^2+X  0  0  X X^2  X X^2+X X^2+X  0  X X^2+X X^2+X X^2+X  X X^2 X^2+X X^2  0  0  0  0 X^2+X

generates a code of length 63 over Z2[X]/(X^3) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+52x^53+134x^54+176x^55+207x^56+316x^57+404x^58+456x^59+590x^60+614x^61+803x^62+816x^63+697x^64+760x^65+542x^66+440x^67+348x^68+236x^69+178x^70+132x^71+109x^72+52x^73+46x^74+24x^75+29x^76+18x^77+5x^78+4x^79+2x^80+1x^92

The gray image is a linear code over GF(2) with n=252, k=13 and d=106.
This code was found by Heurico 1.16 in 5.15 seconds.