The generator matrix

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

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+532x^58+936x^59+1896x^60+1840x^61+2482x^62+1896x^63+2184x^64+1348x^65+1526x^66+764x^67+536x^68+204x^69+134x^70+36x^71+43x^72+16x^73+6x^74+2x^76+2x^80

The gray image is a code over GF(2) with n=504, k=14 and d=232.
This code was found by Heurico 1.16 in 3.06 seconds.