The generator matrix

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

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+44x^57+51x^58+60x^59+85x^60+64x^61+127x^62+1228x^63+129x^64+52x^65+65x^66+36x^67+31x^68+24x^69+13x^70+20x^71+9x^72+8x^73+1x^112

The gray image is a code over GF(2) with n=504, k=11 and d=228.
This code was found by Heurico 1.16 in 0.422 seconds.