The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2  X  1  1  1  1 X^2+X X^2+X  1  1  1 X^2  1  1  1 X^2 X^2  1  1  1  X  1  1  1 X^2+X  1  1  1 X^2+X  1  0  1 X^2+X  1  1 X^2+X  1  1 X^2+X  0  1  1  1 X^2+X  1  1  1  X  1  1  1  1  1 X^2
 0  1  1  0 X^2+X+1  1  X X+1  1  1 X^2+1 X^2+X X^2+X+1  0  1  1  X  1 X+1  1  X  1 X^2  1  1 X^2 X^2+1 X+1  1 X^2+X  1  X  1  X X^2+X  1  1  1  1 X+1  1 X^2  1  1  X X^2+X  1  1 X^2+X X^2+X X^2+1  1  1 X^2 X^2+1  1  1  1  X  0 X^2+X+1  X
 0  0  X  0 X^2+X  0  0  0 X^2 X^2 X^2  0  0  X X^2+X  X  X X^2+X X^2+X X^2+X  X X^2  0 X^2+X  X X^2+X  0 X^2 X^2  X X^2 X^2  X  0 X^2  X  0  X X^2+X  0  X X^2+X  X X^2+X  X  X X^2  0  0  X X^2+X  0  0  X X^2  0 X^2 X^2+X X^2+X  X X^2+X X^2+X
 0  0  0  X  0  0  X X^2 X^2+X  X  0  0  X  X  X  0 X^2 X^2+X X^2+X X^2+X  X  X  X  X X^2  0 X^2 X^2  X  0  X  0 X^2  0 X^2+X X^2 X^2  X  X X^2+X  X X^2+X X^2  0 X^2  0  0 X^2  0  X  X  0 X^2 X^2 X^2 X^2+X X^2  0 X^2+X X^2+X X^2  X
 0  0  0  0 X^2  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2  0  0  0  0  0  0 X^2  0  0 X^2  0 X^2  0 X^2 X^2 X^2  0  0 X^2  0  0 X^2
 0  0  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0  0 X^2  0 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0  0 X^2  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0  0 X^2  0
 0  0  0  0  0  0 X^2  0 X^2  0  0  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0  0  0 X^2 X^2  0 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0  0  0 X^2 X^2  0 X^2 X^2 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+161x^54+84x^55+437x^56+288x^57+713x^58+516x^59+888x^60+584x^61+912x^62+772x^63+794x^64+464x^65+609x^66+284x^67+366x^68+72x^69+120x^70+8x^71+52x^72+42x^74+13x^76+3x^78+8x^80+1x^84

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 5.92 seconds.