The generator matrix

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

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+139x^54+168x^55+481x^56+440x^57+570x^58+592x^59+528x^60+432x^61+419x^62+136x^63+131x^64+24x^65+22x^66+8x^68+1x^70+1x^72+2x^80+1x^94

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 0.297 seconds.