The generator matrix

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

generates a code of length 60 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+82x^51+525x^52+1734x^53+4014x^54+7726x^55+13620x^56+19886x^57+29558x^58+34106x^59+38713x^60+34434x^61+30685x^62+20626x^63+13212x^64+6998x^65+3592x^66+1616x^67+633x^68+224x^69+81x^70+50x^71+13x^72+4x^73+4x^74+3x^76+2x^78+2x^79

The gray image is a code over GF(2) with n=480, k=18 and d=204.
This code was found by Heurico 1.16 in 520 seconds.