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

generates a code of length 59 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+216x^54+104x^55+459x^56+516x^57+544x^58+660x^59+523x^60+344x^61+276x^62+128x^63+184x^64+36x^65+80x^66+4x^67+15x^68+4x^70+1x^76+1x^92

The gray image is a code over GF(2) with n=472, k=12 and d=216.
This code was found by Heurico 1.16 in 0.438 seconds.