The generator matrix

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

generates a code of length 63 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+112x^58+552x^59+862x^60+1236x^61+1168x^62+1180x^63+804x^64+716x^65+546x^66+452x^67+266x^68+164x^69+68x^70+36x^71+9x^72+12x^73+2x^74+4x^75+2x^76

The gray image is a code over GF(2) with n=504, k=13 and d=232.
This code was found by Heurico 1.16 in 0.75 seconds.