The generator matrix

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

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+100x^53+570x^54+944x^55+1374x^56+1448x^57+2146x^58+2272x^59+3063x^60+2904x^61+3194x^62+2884x^63+3088x^64+2504x^65+2076x^66+1372x^67+1269x^68+660x^69+458x^70+204x^71+129x^72+64x^73+28x^74+4x^75+4x^76+6x^78+2x^82

The gray image is a linear code over GF(2) with n=248, k=15 and d=106.
This code was found by Heurico 1.13 in 12.7 seconds.