The generator matrix

 1  0  0  1  1  1  X  1 X+2  1  1  X  1  X  1  1  1  0  0  2  1  1 X+2  1  X  2  1  0  1  1  0  0  1  1  1  1  2  1 X+2  1  X  1 X+2  1  0  1  2 X+2  X  1  1  2  1  1  2  1  X  1  X  1
 0  1  0  0  1 X+3  1  2  0  2 X+3  1 X+1  1  2  3 X+2  1  1  X  1 X+3  1  X  1 X+2  X  1 X+2  3  X  1 X+3  0  X  0  1 X+3  0  3  1  0 X+2 X+3  1  0  0  1  2  2  X  2  1 X+2  1  2  1  1  2  0
 0  0  1  1 X+1  0  1 X+1  1  X X+1  X  0 X+1  3  1  X  2 X+3  1  X X+1 X+3  1  3  1  1  X  0  2  1  0  0 X+3  2 X+2  1 X+1  1 X+3  3 X+1  1  X X+3  3  1  0  1  0  1  1  3 X+3  3  X X+1 X+1  X  0
 0  0  0  X  X X+2  2 X+2  0  0  X  2  0 X+2  2  0 X+2 X+2  X  X  0  2  2 X+2  X X+2  0  X  X  2  2  0  X  2  X X+2  2  0 X+2  0 X+2 X+2  X  2  0 X+2  0  2  0  0  0 X+2  X  X  X X+2  2 X+2  X  0
 0  0  0  0  2  0  0  2  2  2  0  2  0  0  2  2  2  0  2  2  0  2  0  2  2  0  2  0  2  2  0  2  2  0  0  2  2  0  2  0  2  0  2  2  0  0  0  0  0  2  0  0  2  0  2  0  2  2  0  0
 0  0  0  0  0  2  2  0  0  0  0  0  2  2  0  0  0  0  2  0  0  2  0  2  0  2  2  2  0  2  2  2  2  2  2  2  2  2  2  0  0  2  2  0  2  2  2  2  0  2  0  0  0  2  2  2  0  2  2  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+24x^52+178x^53+336x^54+482x^55+640x^56+724x^57+704x^58+746x^59+818x^60+712x^61+670x^62+616x^63+468x^64+364x^65+312x^66+184x^67+75x^68+64x^69+22x^70+16x^71+19x^72+4x^73+4x^74+2x^75+3x^76+2x^77+2x^79

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 3.17 seconds.