The generator matrix

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

generates a code of length 58 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+416x^51+1899x^52+3806x^53+7078x^54+10750x^55+14472x^56+17056x^57+19213x^58+18112x^59+15668x^60+10198x^61+6346x^62+3482x^63+1594x^64+582x^65+249x^66+84x^67+27x^68+20x^69+10x^70+4x^71+3x^72+2x^73

The gray image is a code over GF(2) with n=464, k=17 and d=204.
This code was found by Heurico 1.16 in 136 seconds.