The generator matrix

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

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+144x^55+391x^56+506x^57+652x^58+768x^59+769x^60+750x^61+676x^62+654x^63+610x^64+656x^65+550x^66+304x^67+275x^68+214x^69+132x^70+78x^71+34x^72+18x^73+4x^74+4x^75+2x^82

The gray image is a linear code over GF(2) with n=248, k=13 and d=110.
This code was found by Heurico 1.16 in 2.63 seconds.