The generator matrix

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

generates a code of length 63 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 59.

Homogenous weight enumerator: w(x)=1x^0+180x^59+123x^60+380x^61+132x^62+460x^63+146x^64+312x^65+88x^66+188x^67+17x^68+12x^69+2x^70+4x^71+1x^72+2x^86

The gray image is a code over GF(2) with n=504, k=11 and d=236.
This code was found by Heurico 1.16 in 0.344 seconds.