The generator matrix

 1  0  0  1  1  1 X^3  1  1  1  1 X^2  0  0  1 X^3+X  1  1  1 X^2+X  X  1  1  X X^2+X  1 X^3+X  1  1  1 X^2  1 X^2+X  1 X^2+X  1 X^3+X^2+X X^3 X^3+X^2  1 X^3+X^2+X  1 X^3+X^2 X^3+X  1 X^2+X  X  1  1  1  1 X^3+X  1 X^3+X^2  1  1  1  1  1
 0  1  0 X^3 X^2+1 X^3+X^2+1  1  X X^3+X X^3+X^2+X+1 X^2+X+1  1  1 X^2+X X^3+X^2  1 X^3+X+1 X^3+1 X^3  0  1 X^2+1  1  1  1 X^3+X^2  X X^3+X^2+X X^2+X+1 X^3+X  1  X X^3+X^2  0  1 X^3+X^2+X  1  1  1 X^3+X^2  1 X^3+X^2+X  1  1 X^2  1  1 X^2+X X^3+X^2 X^3 X^3+X^2+X  1 X^2+X+1  1 X^3+1 X^2+X X^2+1 X^3  0
 0  0  1 X^3+X+1 X+1 X^3 X^3+X+1 X^3+X X^3+1  1  X  1 X^3+X  1 X^2+X X^3+X^2+X X^3+X^2+X+1  X X^3+X^2+1  1  1  1 X^3 X+1 X^3+X^2 X^2  1 X^2+1 X^3+X^2 X^3+X^2+X+1 X^2 X^3+X^2  1 X^3+X^2+X X^3+X^2+X X^3+X^2+X+1  1 X^2+1 X^3+X X^2+X+1 X^3+X+1 X^3+X^2+X X^2+X+1 X^3+X^2  0 X^2+X+1  X X^3 X^2+1 X^3+X^2+X+1 X^3+X+1  0 X^3+X+1 X^3+X^2+X X+1 X^3+1 X^3+X^2+1 X^3+X^2  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+144x^55+548x^56+608x^57+796x^58+456x^59+535x^60+248x^61+300x^62+176x^63+137x^64+88x^65+48x^66+8x^67+2x^68+1x^84

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 5.67 seconds.