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 X^2+2  1  1  1  1  1  1  X  1  X  1  1  1  1  1  1  1 X^2+2  X  1  1 X^2+2  X  2  1  1
 0  X  0  X  2  0 X+2  X X^2 X^2+X X^2 X^2+X X^2+2 X^2+X+2 X^2 X^2+X  0  2 X+2 X+2  0 X^2 X+2 X^2+X X^2 X^2+X+2  2 X^2+X X^2+2 X^2+X X^2+2  X  0 X^2  X  X X^2+2 X+2 X+2 X^2+X+2 X^2 X+2 X^2+X+2 X+2  X X^2  0 X^2+X  X X^2+2  0  X  X  2  X  0  2  X X^2+2 X+2
 0  0  X  X X^2 X^2+X X^2+X X^2 X^2 X^2+X+2  X X^2+2  0 X+2 X^2+X  2  0 X^2+X+2 X^2+X X^2+2 X^2+2 X^2+X X+2 X^2+2 X^2+2 X^2+X+2 X+2  2  2 X+2 X+2  0  2 X+2 X^2+X X^2+X+2 X^2+X X+2 X^2 X^2+2  0 X^2+X  0  2 X^2+X  0 X^2 X+2 X^2+2  X  X  2 X^2  X X^2+X+2  X X+2  X X^2 X^2
 0  0  0  2  2  2  0  2  0  2  2  0  2  0  0  2  2  0  2  0  0  2  0  2  2  0  2  0  0  2  0  2  0  2  2  0  0  2  0  2  2  0  0  2  2  0  0  0  0  2  2  2  0  0  2  0  2  0  2  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+162x^56+112x^57+275x^58+340x^59+354x^60+350x^61+194x^62+76x^63+102x^64+16x^65+43x^66+20x^68+2x^69+1x^104

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 0.281 seconds.