The generator matrix

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

generates a code of length 59 over Z4[X]/(X^2+2) 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 code over GF(2) with n=472, k=12 and d=212.
This code was found by Heurico 1.16 in 0.531 seconds.