The generator matrix

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

generates a code of length 59 over Z2[X]/(X^4) who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+302x^55+454x^56+554x^57+553x^58+536x^59+543x^60+516x^61+251x^62+194x^63+97x^64+46x^65+10x^66+24x^67+8x^68+4x^69+1x^70+1x^76+1x^82

The gray image is a linear code over GF(2) with n=472, k=12 and d=220.
This code was found by Heurico 1.16 in 1.56 seconds.