The generator matrix

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

generates a code of length 60 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+168x^52+88x^53+412x^54+316x^55+694x^56+472x^57+944x^58+660x^59+926x^60+656x^61+738x^62+484x^63+657x^64+312x^65+320x^66+76x^67+138x^68+8x^69+64x^70+32x^72+16x^74+8x^76+2x^78

The gray image is a code over GF(2) with n=240, k=13 and d=104.
This code was found by Heurico 1.16 in 4.05 seconds.