The generator matrix

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

generates a code of length 59 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+346x^54+1142x^55+1691x^56+1956x^57+2392x^58+2044x^59+2158x^60+1664x^61+1306x^62+886x^63+403x^64+188x^65+110x^66+40x^67+34x^68+16x^69+4x^70+1x^72+2x^74

The gray image is a code over GF(2) with n=472, k=14 and d=216.
This code was found by Heurico 1.16 in 2.64 seconds.