The generator matrix

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

generates a code of length 62 over Z2[X]/(X^3) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+101x^52+258x^53+486x^54+744x^55+1157x^56+1536x^57+2045x^58+2464x^59+2720x^60+3286x^61+3175x^62+3100x^63+3025x^64+2540x^65+2136x^66+1498x^67+967x^68+626x^69+382x^70+226x^71+135x^72+68x^73+27x^74+30x^75+20x^76+6x^77+5x^78+2x^79+2x^80

The gray image is a linear code over GF(2) with n=248, k=15 and d=104.
This code was found by Heurico 1.16 in 42.5 seconds.