The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+286x^53+970x^54+2080x^55+2716x^56+3810x^57+4637x^58+4262x^59+4652x^60+3558x^61+2564x^62+1668x^63+797x^64+480x^65+133x^66+82x^67+24x^68+22x^69+8x^70+4x^71+10x^72+2x^73+2x^77

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 9.12 seconds.