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

generates a code of length 63 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+41x^56+34x^58+278x^60+216x^62+1024x^63+193x^64+152x^66+30x^68+32x^70+20x^72+14x^74+12x^76+1x^120

The gray image is a code over GF(2) with n=504, k=11 and d=224.
This code was found by Heurico 1.16 in 0.328 seconds.