The generator matrix

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

generates a code of length 62 over Z2[X]/(X^3) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+216x^53+513x^54+812x^55+1184x^56+1744x^57+2045x^58+2512x^59+2784x^60+2992x^61+3298x^62+2940x^63+2883x^64+2532x^65+2126x^66+1522x^67+1024x^68+772x^69+373x^70+254x^71+116x^72+60x^73+29x^74+22x^75+8x^76+4x^77+2x^79

The gray image is a linear code over GF(2) with n=248, k=15 and d=106.
This code was found by Heurico 1.16 in 40 seconds.