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

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+103x^56+112x^57+308x^58+400x^59+311x^60+512x^61+72x^62+16x^63+48x^64+112x^65+52x^66+1x^116

The gray image is a code over GF(2) with n=480, k=11 and d=224.
This code was found by Heurico 1.16 in 0.25 seconds.