The generator matrix

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

generates a code of length 63 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+60x^58+660x^59+880x^60+1162x^61+1069x^62+1164x^63+930x^64+836x^65+462x^66+424x^67+222x^68+158x^69+78x^70+56x^71+7x^72+20x^73+2x^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 0.688 seconds.