The generator matrix

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

generates a code of length 60 over Z4[X]/(X^2+2X+2) 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.