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

generates a code of length 60 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+7x^56+16x^57+16x^58+48x^59+848x^60+48x^61+16x^62+16x^63+7x^64+1x^120

The gray image is a code over GF(2) with n=480, k=10 and d=224.
This code was found by Heurico 1.16 in 0.203 seconds.