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

generates a code of length 60 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+24x^57+60x^58+104x^59+653x^60+104x^61+44x^62+24x^63+9x^64+1x^116

The gray image is a code over GF(2) with n=480, k=10 and d=228.
This code was found by Heurico 1.16 in 19.2 seconds.