The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+71x^54+146x^55+181x^56+396x^57+315x^58+818x^59+447x^60+678x^61+279x^62+350x^63+160x^64+130x^65+46x^66+22x^67+21x^68+10x^69+5x^70+8x^71+6x^72+2x^73+3x^74+1x^94

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 0.547 seconds.