The generator matrix

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

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+38x^54+520x^55+911x^56+1158x^57+1321x^58+1118x^59+886x^60+734x^61+553x^62+478x^63+262x^64+108x^65+53x^66+40x^67+4x^68+1x^70+4x^71+2x^74

The gray image is a code over GF(2) with n=472, k=13 and d=216.
This code was found by Heurico 1.16 in 0.64 seconds.