The generator matrix

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

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+126x^53+558x^54+1010x^55+1747x^56+2286x^57+3434x^58+3798x^59+5099x^60+5158x^61+6487x^62+5894x^63+6469x^64+5418x^65+5585x^66+3732x^67+3332x^68+2172x^69+1491x^70+858x^71+443x^72+184x^73+133x^74+62x^75+29x^76+16x^77+8x^78+6x^79

The gray image is a linear code over GF(2) with n=252, k=16 and d=106.
This code was found by Heurico 1.13 in 49.6 seconds.