The generator matrix

 1  0  0  1  1  1  X  1 X^2+X  1  1  X  1 X^2+X  1  X X^2  1  1  0  1  X  1  1  X  1  1  0  1  X  1  1  0  X  1  0  0 X^2+X  1  1  0  1  1  1  1 X^2  1 X^2 X^2 X^2+X  0  1 X^2  1  1 X^2+X  X  0  1  1  0  1
 0  1  0  0  1 X^2+X+1  1 X^2  0 X^2 X^2+X+1  1 X+1  1  1 X^2+X  1  X  X  1  X  1 X^2+X+1 X+1  1  X  0  1 X^2 X^2 X^2+1 X+1 X^2+X X^2 X+1  1  1  1  1  0  X  0 X^2+X X+1  1  1  X  1  1  1  1  1 X^2 X^2+X+1  0  1 X^2+X  1 X^2+1 X^2+X  1  0
 0  0  1  1 X+1  0  1 X+1  1  X X+1  X  X X+1 X^2+1  1  X X^2+X  0 X+1 X+1 X^2  X X^2+X+1 X^2+1  1 X^2 X^2+X X+1  1  0  0  1  1 X+1 X^2+X X^2 X+1  0  1  1 X^2+X+1  X  0 X^2+X X^2+X+1  0 X^2+1  0 X^2+1 X^2+X+1 X^2+X  1 X^2+X X^2+X X^2+X  1 X+1 X^2+1 X^2+1 X^2+X+1  0
 0  0  0  X  X X^2+X X^2 X^2+X  0  0  X X^2  X  0 X^2+X  0  0 X^2 X^2 X^2 X^2+X X^2  0 X^2 X^2+X X^2 X^2+X X^2+X X^2 X^2+X  X  0 X^2+X  X X^2+X  X  X X^2+X X^2  0  0  X  X X^2+X  0 X^2  0  X X^2+X X^2+X  0 X^2  0 X^2 X^2+X  X X^2 X^2 X^2+X X^2 X^2  0
 0  0  0  0 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0  0 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0
 0  0  0  0  0 X^2 X^2  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2  0  0  0 X^2 X^2  0 X^2  0  0  0 X^2 X^2  0 X^2  0  0 X^2 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+49x^54+148x^55+415x^56+440x^57+635x^58+624x^59+903x^60+644x^61+753x^62+578x^63+786x^64+604x^65+591x^66+354x^67+299x^68+122x^69+132x^70+44x^71+26x^72+8x^73+10x^74+10x^75+2x^76+6x^77+6x^78+2x^79

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 3.02 seconds.