The generator matrix

 1  0  0  0  1  1  1  X  1  1 X^2+X X^2  1  1 X^2  1  1  1 X^2  1  1 X^2+X  1  0  1  1  X  0  1  1 X^2+X X^2+X X^2+X  0 X^2  1  1  1  1  0  1  1  1 X^2+X  1  1  1  1  1  0  1  X  0 X^2  1  1  1  1  0 X^2  1  1
 0  1  0  0  1  X  1  1 X^2 X^2+X  1  1 X^2+1 X+1 X^2+X  1 X+1 X^2  1  1 X^2+X+1  1  0  1  0  X X^2  X  1 X^2  1  1  X X^2+X  1 X^2+X+1 X^2+X+1  1  X  1  0  0  0 X^2  0 X^2+X X^2+1 X^2+1  1  1  1 X^2+X X^2+X  0 X^2+X+1 X^2+X+1 X^2+1 X+1  1 X^2+X  0  0
 0  0  1  0  X  1 X+1  1  1 X^2 X^2+X+1  0 X+1  X  1  X  1  0 X^2+1 X^2+X X+1 X^2 X^2+X X^2 X^2+1 X+1  1 X^2+X  1 X^2+1 X^2+X+1  X  1  1 X+1 X^2  1  0 X^2+X+1 X^2+1 X^2+X+1 X^2 X^2+X  1  0 X^2 X^2+X  X X^2  0 X^2+X  1  1  1 X+1 X^2+X X^2+1  X X^2+1  1 X^2+1 X^2
 0  0  0  1  X X^2+X X^2 X^2+X  1  1 X+1 X^2+X+1  1 X^2+X+1 X+1  0  0 X+1  1 X^2+X+1 X+1  1  0 X^2+X  1  X X^2+X  1 X^2+1 X^2  X X+1  0 X^2+X+1  X X^2+X+1  X  X  1 X+1 X^2+1 X^2+X  1 X^2+1 X^2+X+1 X^2 X+1  1 X^2+X  1  X  X  0 X+1 X^2+1  X  0 X^2  X  X X^2+X  X
 0  0  0  0 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2  0  0  0 X^2 X^2 X^2  0 X^2  0  0  0 X^2 X^2 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+170x^55+344x^56+562x^57+656x^58+774x^59+685x^60+706x^61+687x^62+752x^63+557x^64+726x^65+447x^66+402x^67+294x^68+160x^69+133x^70+74x^71+22x^72+20x^73+13x^74+4x^75+1x^76+2x^77

The gray image is a linear code over GF(2) with n=248, k=13 and d=110.
This code was found by Heurico 1.11 in 1 seconds.