The generator matrix

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

generates a code of length 62 over Z2[X]/(X^3) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+48x^54+172x^55+286x^56+584x^57+533x^58+814x^59+668x^60+818x^61+658x^62+818x^63+565x^64+638x^65+439x^66+486x^67+250x^68+178x^69+92x^70+74x^71+20x^72+18x^73+19x^74+4x^75+2x^76+4x^77+2x^78+1x^82

The gray image is a linear code over GF(2) with n=248, k=13 and d=108.
This code was found by Heurico 1.16 in 3.25 seconds.