The generator matrix

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

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+34x^52+48x^53+120x^54+166x^55+290x^56+422x^57+417x^58+628x^59+816x^60+764x^61+894x^62+848x^63+632x^64+600x^65+493x^66+364x^67+221x^68+212x^69+96x^70+42x^71+32x^72+2x^73+15x^74+14x^76+10x^78+5x^80+3x^82+3x^84

The gray image is a linear code over GF(2) with n=248, k=13 and d=104.
This code was found by Heurico 1.16 in 3.82 seconds.