The generator matrix

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

generates a code of length 58 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+642x^55+664x^56+768x^57+583x^58+464x^59+324x^60+240x^61+111x^62+146x^63+41x^64+96x^65+1x^66+12x^67+1x^68+1x^70+1x^76

The gray image is a code over GF(2) with n=464, k=12 and d=220.
This code was found by Heurico 1.16 in 114 seconds.