The generator matrix

 1  0  1  1  1  X  1  1 X^2+X+2  1  1 X^2+X X^2+X+2 X^2  1  1 X^2  1  1  1  1  0  1  1  1  X  1  1  1  1  X  1  2  1  1  1 X^2  0 X^2+2 X+2 X^2+X+2  1  1  1  1  1  1  1 X^2+2  1  1  1  1 X^2  0  1  1 X^2+X  1  1
 0  1  1 X^2 X+1  1  X  3  1 X+2 X^2+X+1  1  1  1 X^2 X^2+3  1  2 X^2+1 X^2+X+3  X  1 X+2 X^2+1 X^2+1  1 X+3 X+1  2 X^2+X+1  1 X^2+X+2  1 X^2+2  1 X^2+X+2  1  1  1  1  1  2 X^2  1 X^2+X X^2+X+3 X^2+X X+1 X^2 X+3 X+1 X^2+1  1  1  1 X^2+1  1  1 X+2  2
 0  0  X X+2  2 X+2 X+2  2 X^2+X+2  0  X  0 X^2+2 X^2 X^2+X+2 X^2+2 X+2 X^2+2 X^2+X+2  2 X^2 X^2+X X^2+X  0 X+2  0  X X^2 X+2 X^2+X X^2+X+2  X X^2+2 X^2 X^2 X^2 X^2+X+2  X  2 X^2+2 X+2 X^2+X+2  2 X^2+X  0 X^2 X^2+X+2 X^2+X  X X^2+X X^2+X+2  2 X^2+2  X X^2+X+2 X^2 X+2 X^2  X  X

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+296x^57+411x^58+288x^59+229x^60+202x^61+291x^62+208x^63+49x^64+42x^65+8x^66+20x^67+1x^74+1x^80+1x^82

The gray image is a code over GF(2) with n=480, k=11 and d=228.
This code was found by Heurico 1.16 in 0.484 seconds.