The generator matrix

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

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+151x^52+426x^53+693x^54+850x^55+1239x^56+1218x^57+1504x^58+1374x^59+1585x^60+1458x^61+1626x^62+1176x^63+1054x^64+694x^65+567x^66+320x^67+204x^68+132x^69+54x^70+22x^71+18x^72+8x^73+1x^74+2x^75+4x^76+3x^78

The gray image is a code over GF(2) with n=240, k=14 and d=104.
This code was found by Heurico 1.13 in 3.98 seconds.