The generator matrix

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

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+75x^54+218x^55+487x^56+452x^57+665x^58+344x^59+650x^60+436x^61+470x^62+200x^63+72x^64+8x^65+4x^66+4x^67+3x^68+1x^70+2x^71+2x^72+1x^82+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 0.312 seconds.