The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+35x^60+16x^61+4x^62+7x^64+1x^68

The gray image is a code over GF(2) with n=480, k=6 and d=240.
This code was found by Heurico 1.16 in 0.125 seconds.