The generator matrix

 1  0  1  1  1 X^3+X^2+X  1  X  1 X^3+X^2  1  1  1 X^3  1  1 X^3+X^2+X  1  1  1 X^2+X  1 X^2  1 X^3+X  1  1  1  1  1 X^2  1  1  1 X^3+X  1  1  1  1  1 X^3+X  1  X  1  1  X  1  1 X^3+X X^3+X^2 X^3+X^2+X X^3+X^2+X  1  1  1  1 X^3+X^2+X  0  1
 0  1 X+1 X^2+X X^3+X^2+1  1 X^3+X^2  1 X^2+X+1  1 X^3+X^2+X X^2+1  X  1 X^3+1  0  1 X^3+X+1 X^3+X  1  1 X^3  1 X^2+1  1 X^2 X^3+1 X+1 X^3+X^2+X+1 X^3+X  1  1 X^2+X+1  0  1 X^3+1 X+1 X^3+X^2+X+1 X^3+X^2+1 X^3  1 X+1 X^3+X^2+X X^2+X+1 X^3+X+1 X^2 X^3+1  1  1  1  1  1 X^3+X^2+1 X^2+1 X^3+X+1 X^3+X^2+X  1  0  0
 0  0 X^2  0 X^3+X^2 X^2  0 X^2 X^3+X^2 X^3 X^2  0 X^3+X^2 X^3+X^2 X^3 X^3 X^3+X^2 X^3+X^2 X^3 X^2  0 X^2 X^2  0 X^3 X^3+X^2 X^3  0  0  0 X^3+X^2 X^2 X^2 X^3+X^2 X^3 X^2 X^3 X^3 X^3+X^2 X^3+X^2 X^3 X^2 X^3  0  0 X^3+X^2  0  0 X^3+X^2 X^3 X^3+X^2 X^3 X^3 X^3 X^3+X^2 X^2  0 X^2  0
 0  0  0 X^3  0  0  0  0 X^3  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3  0  0 X^3  0  0  0  0  0  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3  0 X^3  0 X^3 X^3  0  0  0
 0  0  0  0 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3  0  0  0 X^3 X^3 X^3  0  0 X^3  0 X^3  0 X^3 X^3 X^3  0  0 X^3  0  0  0 X^3  0  0 X^3  0 X^3  0  0 X^3 X^3  0 X^3  0  0  0 X^3  0  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+93x^54+218x^55+568x^56+380x^57+608x^58+404x^59+740x^60+334x^61+378x^62+156x^63+157x^64+20x^65+5x^66+18x^67+3x^68+2x^69+2x^71+2x^72+3x^74+2x^75+1x^78+1x^84

The gray image is a linear code over GF(2) with n=472, k=12 and d=216.
This code was found by Heurico 1.16 in 0.359 seconds.