The generator matrix

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

generates a code of length 60 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+78x^53+158x^54+274x^55+231x^56+478x^57+315x^58+496x^59+190x^60+484x^61+289x^62+408x^63+200x^64+204x^65+100x^66+92x^67+10x^68+30x^69+22x^70+6x^71+7x^72+6x^73+9x^74+4x^75+3x^78+1x^80

The gray image is a code over GF(2) with n=240, k=12 and d=106.
This code was found by Heurico 1.16 in 80.3 seconds.