The generator matrix

 1  0  0  1  1  1 X^2  0 X^3 X^2  1  1  1  1  X  1  X  1 X^3+X  1  1  X  1 X^2+X  1  1  1  1  1 X^3  1 X^2+X  1  1  1  1 X^3+X^2+X  1 X^2+X  1 X^3+X^2  1  1  1  1  1 X^3+X^2+X  0 X^3  1  1  1  1 X^3+X^2  1  1 X^2+X  0  1
 0  1  0 X^2 X^3+X^2+1  1  1 X^2+X  1  1  0 X^3+X^2  1 X^2+1 X^3+X X^3+X^2+X  1 X+1  1 X^2+X+1 X^3+X^2+X X^3 X^3+X+1  1 X^3+X X^3+X^2+1 X^3+X^2+X X^2+X+1 X^3+X^2 X^3+X  1  1 X^2+X X^3+X^2+X+1  0 X^3+1  1  1  1 X^3  1 X^3+X X^2 X^2+X X^2 X^3+X+1  1  1  1  0 X^3+X X^3+X^2+X+1 X^3+X^2+1 X^2 X^3+X^2 X^3+X^2+1  1 X^3+X^2  0
 0  0  1 X^2+X+1 X^3+X^2+X+1 X^2 X^2+X+1  1 X^3+X^2+X  1 X^2+X  1  X X^3+X^2+1  1  X X^2+X+1 X^2+1 X^3+X X^3  1  1 X^3+X^2+X X^2 X^2+X+1 X^3+1  0 X^2+1 X+1  1 X^3+X+1 X^3+X^2+1 X^3+1 X^3+X+1 X^3+X^2 X^2+X X^2+X+1  0 X^3 X^2+1  X X^3+X^2  X X^2 X^2 X^3+X^2 X^3+1 X^3+X^2 X^3+X^2+X+1 X^2+X+1 X^3+X^2+X X^3+1 X^3+X^2+X  1 X^2+1 X^2+1 X+1  1  0
 0  0  0 X^3 X^3  0 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3  0 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3  0 X^3  0  0  0  0  0  0  0 X^3 X^3  0  0 X^3  0 X^3  0  0  0 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3 X^3  0  0 X^3  0

generates a code of length 59 over Z2[X]/(X^4) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+31x^54+606x^55+914x^56+1166x^57+1110x^58+1180x^59+850x^60+924x^61+511x^62+410x^63+221x^64+154x^65+57x^66+28x^67+10x^68+12x^69+2x^70+4x^72+1x^74

The gray image is a linear code over GF(2) with n=472, k=13 and d=216.
This code was found by Heurico 1.16 in 2.67 seconds.