The generator matrix

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

generates a code of length 62 over Z2[X]/(X^3) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+30x^58+156x^59+308x^60+208x^61+36x^62+20x^63+15x^64+20x^65+10x^66+80x^67+92x^68+28x^69+16x^70+4x^74

The gray image is a linear code over GF(2) with n=248, k=10 and d=116.
This code was found by Heurico 1.16 in 0.136 seconds.