The generator matrix

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

generates a code of length 63 over Z2[X]/(X^3) who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+160x^55+498x^56+694x^57+1027x^58+1006x^59+1349x^60+1276x^61+1525x^62+1472x^63+1584x^64+1370x^65+1302x^66+856x^67+852x^68+588x^69+367x^70+176x^71+147x^72+44x^73+33x^74+26x^75+17x^76+12x^77+2x^78

The gray image is a linear code over GF(2) with n=252, k=14 and d=110.
This code was found by Heurico 1.13 in 3.67 seconds.