The generator matrix

 1  0  0  1  1  1 X^2+X  1 X^2  1  X  1  1 X^2  1 X^2  1  1  1 X^2  X  0  1 X^2 X^2+X  1  1  1  1  1 X^2+X  X  1  X X^2+X  X  1  1  1  1  1  0  1  1  1  0  0  1  1  1 X^2  1  0  0  1  1  1 X^2+X X^2+X  X X^2  0  1
 0  1  0  0  1  1  1  X  1  X  1 X+1  1  X X+1  0  1  X X^2  1  1  1 X^2+X+1  1  X X^2  1 X^2  0  X X^2+X X^2+X  1  1  1  1 X^2+X+1 X+1  0 X^2 X+1  X X^2+1 X^2+1 X+1 X^2+X  1 X^2  X X^2+1  1  0  1 X^2 X^2+X+1 X^2+1  1  1  1  X  1  1 X^2+X+1
 0  0  1  1  1  0  1 X+1  X  X X^2+1  X  1  1 X+1  1  X X^2+1  X  X  1  X  X X^2+X+1  1 X^2+X+1 X+1 X^2+X X^2+X+1 X^2  1  1 X+1 X+1 X^2 X^2+X X^2+1 X^2 X^2+X X+1 X^2+X  1 X^2+X+1 X^2+X  X  1 X+1 X+1  0  1 X^2 X^2+1  0  1 X^2  1 X^2+X+1  0 X+1  1  X X^2 X^2
 0  0  0  X  0  0  0  0  X X^2+X X^2+X X^2+X X^2  X X^2+X  0  0 X^2 X^2  X  X  0  X  0  X X^2+X  X  X  0 X^2+X X^2 X^2 X^2+X  X  0  X X^2  X X^2+X  X X^2 X^2+X X^2+X  X X^2  0  0  X  X  X X^2+X X^2 X^2  X X^2 X^2+X  0 X^2+X  X  X  0  0  0
 0  0  0  0  X  0  0  0  0  0  0  0  0 X^2 X^2  X  X  X  X X^2+X  X X^2+X  X  X X^2+X  X X^2+X  X  X X^2  0  X X^2+X X^2+X X^2  X  0 X^2 X^2 X^2+X X^2 X^2  0 X^2+X X^2+X X^2+X X^2  X X^2+X X^2+X X^2+X X^2  X X^2 X^2 X^2+X X^2+X  0  X X^2+X X^2  X X^2+X
 0  0  0  0  0  X X^2+X X^2+X X^2+X  X  0 X^2  0  X  X X^2 X^2+X  X X^2  X  0 X^2  0  X X^2+X  0  X X^2+X  X X^2+X X^2 X^2  X X^2+X  X X^2  X  X X^2 X^2+X X^2 X^2  0  0  0  X  0  X  0 X^2 X^2+X X^2 X^2+X  X  0  X X^2+X  0  0 X^2 X^2+X X^2+X 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+72x^53+277x^54+462x^55+803x^56+1282x^57+1536x^58+2002x^59+2375x^60+2748x^61+3203x^62+3200x^63+3241x^64+2842x^65+2487x^66+2148x^67+1452x^68+1096x^69+636x^70+346x^71+243x^72+138x^73+73x^74+34x^75+41x^76+12x^77+12x^78+4x^80+2x^81

The gray image is a linear code over GF(2) with n=252, k=15 and d=106.
This code was found by Heurico 1.16 in 44 seconds.