The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+54x^58+700x^59+746x^60+1414x^61+908x^62+1260x^63+676x^64+996x^65+410x^66+492x^67+220x^68+198x^69+29x^70+60x^71+21x^72+6x^74+1x^78

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 0.718 seconds.