The generator matrix

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

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+45x^52+224x^53+336x^54+486x^55+552x^56+728x^57+576x^58+952x^59+634x^60+852x^61+596x^62+662x^63+466x^64+440x^65+242x^66+182x^67+79x^68+52x^69+34x^70+20x^71+12x^72+8x^73+6x^74+2x^75+2x^76+2x^78+1x^80

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 2.79 seconds.