The generator matrix

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

generates a code of length 60 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+16x^54+170x^55+124x^56+482x^57+376x^58+636x^59+517x^60+644x^61+358x^62+434x^63+123x^64+186x^65+12x^66+8x^67+2x^68+1x^70+4x^74+1x^76+1x^86

The gray image is a code over GF(2) with n=480, k=12 and d=216.
This code was found by Heurico 1.16 in 0.297 seconds.