The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+117x^54+308x^55+370x^56+398x^57+451x^58+442x^59+359x^60+318x^61+306x^62+222x^63+215x^64+228x^65+123x^66+86x^67+71x^68+30x^69+27x^70+14x^71+8x^72+2x^73

The gray image is a code over GF(2) with n=240, k=12 and d=108.
This code was found by Heurico 1.16 in 0.615 seconds.