The generator matrix

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

generates a code of length 62 over Z2[X]/(X^3) who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+72x^55+186x^56+254x^57+318x^58+328x^59+354x^60+402x^61+384x^62+416x^63+375x^64+278x^65+224x^66+182x^67+143x^68+70x^69+24x^70+14x^71+20x^72+20x^73+10x^74+10x^75+6x^76+2x^79+2x^80+1x^84

The gray image is a linear code over GF(2) with n=248, k=12 and d=110.
This code was found by Heurico 1.16 in 0.906 seconds.