The generator matrix

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

generates a code of length 58 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+177x^54+628x^55+469x^56+628x^57+581x^58+552x^59+364x^60+328x^61+152x^62+100x^63+21x^64+68x^65+24x^66+1x^72+1x^74+1x^78

The gray image is a code over GF(2) with n=464, k=12 and d=216.
This code was found by Heurico 1.16 in 0.313 seconds.