The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 X^2  1  1  1  1  0  1  1  1  1  1  X  1  1  X  1  X  1 X^3+X^2  1  X  1  1  1 X^3  1  1  1  1  X  1  1
 0  X  0  X X^3  0 X^2+X X^3+X^2+X  0 X^3 X^3+X X^3+X  0 X^3+X^2+X X^3+X^2  X X^3+X^2 X^2+X X^2+X X^3+X^2 X^3+X^2+X X^3+X X^3+X^2 X^2 X^3+X X^3+X^2 X^3+X X^3  0 X^2 X^2+X X^2+X  X  0 X^2 X^3+X^2+X X^3+X^2+X X^2  X  0 X^3 X^3+X X^3+X^2 X^3+X^2+X  0  X X^2 X^3+X^2  X X^3+X X^3  X X^3 X^2+X X^3+X  X X^2 X^3+X^2 X^2+X
 0  0  X  X  0 X^3+X^2+X X^2+X X^3 X^2 X^3+X^2+X X^3+X^2+X X^2 X^3+X^2 X^2  X  X X^3+X^2+X X^3+X  0 X^3  X  0 X^3+X X^2  0 X^3 X^2+X  X X^2+X X^3+X^2 X^3+X X^2  X  X X^3+X^2+X X^3+X^2+X X^2  0 X^2+X X^3 X^3+X^2+X X^3+X^2+X X^3+X^2 X^3+X^2 X^2 X^3+X^2+X  X  X X^3+X^2  0  X X^2 X^3+X  X X^3+X^2 X^3 X^3+X^2+X X^3+X  X
 0  0  0 X^2 X^3+X^2 X^2 X^3 X^2 X^2  0 X^2 X^3+X^2  0  0 X^3+X^2 X^3 X^2 X^3+X^2  0 X^2  0 X^2  0  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^3+X^2 X^2 X^3  0 X^3 X^3+X^2 X^3+X^2 X^3 X^3 X^3 X^3  0 X^3+X^2  0  0 X^3+X^2  0 X^3+X^2 X^3 X^2 X^3+X^2 X^3 X^3 X^3 X^3 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+168x^54+188x^55+333x^56+436x^57+712x^58+620x^59+671x^60+376x^61+208x^62+96x^63+126x^64+64x^65+60x^66+8x^67+20x^68+4x^69+4x^70+1x^100

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 0.438 seconds.