The generator matrix

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

generates a code of length 59 over Z2[X]/(X^4) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+54x^53+144x^54+228x^55+355x^56+514x^57+513x^58+576x^59+630x^60+378x^61+271x^62+202x^63+67x^64+68x^65+45x^66+14x^67+10x^68+6x^69+2x^71+9x^72+2x^73+2x^74+2x^75+2x^77+1x^86

The gray image is a linear code over GF(2) with n=472, k=12 and d=212.
This code was found by Heurico 1.16 in 0.531 seconds.