The generator matrix

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

generates a code of length 60 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+132x^50+434x^51+996x^52+1578x^53+2245x^54+3096x^55+4202x^56+4544x^57+6055x^58+5958x^59+6626x^60+6456x^61+5926x^62+4986x^63+4317x^64+2824x^65+2214x^66+1352x^67+830x^68+358x^69+177x^70+134x^71+50x^72+16x^73+17x^74+8x^75+2x^80+2x^82

The gray image is a code over GF(2) with n=240, k=16 and d=100.
This code was found by Heurico 1.13 in 54.4 seconds.