The generator matrix

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

generates a code of length 59 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+286x^53+926x^54+2160x^55+2738x^56+3994x^57+4068x^58+4954x^59+3982x^60+3816x^61+2522x^62+1760x^63+826x^64+464x^65+120x^66+78x^67+44x^68+14x^69+4x^70+8x^71+1x^72+2x^73

The gray image is a code over GF(2) with n=472, k=15 and d=212.
This code was found by Heurico 1.16 in 9.52 seconds.