The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2+2  1 X+2  1  1  1  0  1  1 X^2+X X^2+2  1  1  1  1 X+2  1  1  0  1  1 X^2+X X+2  1  1  1 X^2+2  1  1  1  0  1  1 X^2+X  X  1  1  1  1  1 X^2+2 X^2+2  1  1  X  1  1  1  X  1  1  1  1 X^2+X X^2+X+2
 0  1 X+1 X^2+X X^2+1  1 X^2+2 X^2+X+3  1 X+2  1  3  0 X+1  1 X^2+X X^2+1  1  1 X^2+2 X^2+X+3 X+2  3  1 X^2+X X+1  1 X^2+2 X^2+1  1  1  0  3 X+2  1 X^2+1 X^2+X+3  0  1 X^2+X X+1  1  0  2 X^2+X+2 X+2 X^2+2 X^2+2  1  1 X^2+X+3  X X+2 X^2+3 X^2+X X+1  X X+2  X  3 X^2+X+2  1  1
 0  0  2  0  0  0  0  0  2  2  0  0  2  2  2  0  0  2  2  0  2  2  0  0  2  2  0  2  2  0  0  2  0  0  0  2  0  2  2  2  0  2  0  2  0  2  0  2  2  2  2  0  0  2  0  2  0  0  0  2  2  2  0
 0  0  0  2  0  0  0  0  2  2  2  2  0  2  0  0  2  2  0  2  2  0  0  0  2  0  2  2  0  0  2  2  0  0  2  0  2  0  2  0  2  2  0  2  2  0  2  2  0  0  2  0  0  2  2  0  0  2  0  2  0  0  2
 0  0  0  0  2  0  0  2  0  0  0  2  2  2  2  2  0  2  0  2  0  0  0  2  2  2  2  0  2  0  2  2  2  0  0  0  2  0  2  2  0  0  2  2  2  2  0  0  2  0  0  2  0  2  2  0  2  2  0  0  0  0  0
 0  0  0  0  0  2  2  2  2  0  2  0  0  0  2  0  2  0  0  2  2  2  0  2  2  2  0  0  2  0  0  2  2  2  2  0  0  2  0  0  2  2  0  0  2  2  0  2  0  2  0  2  2  2  0  2  0  2  0  0  0  2  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+145x^58+176x^59+553x^60+336x^61+623x^62+480x^63+581x^64+416x^65+478x^66+112x^67+137x^68+16x^69+32x^70+5x^72+1x^78+1x^80+2x^84+1x^90

The gray image is a code over GF(2) with n=504, k=12 and d=232.
This code was found by Heurico 1.16 in 0.344 seconds.