The generator matrix

 1  0  0  0  1  1  1  X X+2  1  1  1 X+2  0  1  0  2  1  1  X  1  1  1  0  1  1  1 X+2 X+2  1  0 X+2  X  1  1  0  2  0  2  1  1  0  1  2 X+2  1 X+2  X  1  1  1  1  X  2  X  X X+2 X+2  1  1
 0  1  0  0  X  0 X+2 X+2  1  3  3  3  1  1 X+1 X+2  1 X+3  2  1  2 X+1 X+1  1  1  0  0  1 X+2  0  1  1 X+2  2  X  X  0 X+2  1 X+3 X+1  2  X  X  1  1  X  1 X+1  0  X  1  1 X+2  1  1  X  2 X+3  X
 0  0  1  0  X  1 X+3  1  3 X+2  3  2  0 X+3  1  1  0  0  X X+3 X+3  2  3  0 X+3  X X+3 X+1  1  1  1  3  1  0  X  1 X+2  1  1  2  1  1 X+3  2 X+1 X+1 X+2  1  2 X+3  3  1  2  1  0  X  1  1 X+1  0
 0  0  0  1 X+1  1  X X+3  0  2  0 X+3 X+3 X+1  3  0 X+2 X+2 X+2  3  0 X+1  X X+3  1 X+1 X+2 X+2  3  1 X+3  X  2 X+2 X+3  2  1  3  2  X  3 X+3  1  1 X+3  2  1  X  1  2 X+1 X+1  2 X+1  2  2  X X+2  1  X
 0  0  0  0  2  0  2  2  2  2  0  0  2  0  2  0  0  2  0  0  2  0  0  2  0  2  0  0  0  2  2  0  2  2  0  2  2  2  2  0  2  0  0  0  0  0  2  2  2  2  0  2  0  2  2  2  2  2  0  2
 0  0  0  0  0  2  2  2  2  0  2  0  0  2  2  2  2  2  2  0  0  2  0  2  2  2  0  2  2  2  0  0  0  0  2  2  0  0  0  0  0  0  0  2  0  0  0  0  0  2  2  2  2  2  0  2  0  0  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+155x^52+440x^53+750x^54+850x^55+1122x^56+1164x^57+1547x^58+1364x^59+1712x^60+1506x^61+1481x^62+1146x^63+1004x^64+804x^65+631x^66+262x^67+216x^68+114x^69+69x^70+22x^71+13x^72+4x^73+2x^74+2x^75+1x^76+2x^79

The gray image is a code over GF(2) with n=240, k=14 and d=104.
This code was found by Heurico 1.16 in 10 seconds.