The generator matrix

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

generates a code of length 59 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+384x^51+1637x^52+3984x^53+7267x^54+13854x^55+19530x^56+29738x^57+33885x^58+40000x^59+35455x^60+30522x^61+19868x^62+13444x^63+6773x^64+3664x^65+1273x^66+510x^67+210x^68+74x^69+43x^70+12x^71+10x^72+2x^73+2x^75+2x^79

The gray image is a code over GF(2) with n=472, k=18 and d=204.
This code was found by Heurico 1.16 in 502 seconds.