The generator matrix

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

generates a code of length 63 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+394x^57+1114x^58+2066x^59+2795x^60+3916x^61+4234x^62+4296x^63+4020x^64+3830x^65+2526x^66+1902x^67+935x^68+402x^69+174x^70+68x^71+33x^72+16x^73+32x^74+4x^75+6x^76+2x^77+2x^80

The gray image is a code over GF(2) with n=504, k=15 and d=228.
This code was found by Heurico 1.16 in 9.44 seconds.