The generator matrix

 1  0  0  1  1  1 X+2  1  1  0  X  1  1  X  1  2  1  1  X  0  1 X+2  1  1  X X+2  1  1  1  X  1  1  2  1  1  0  1  2  1  0  2  0  1  2  X  1  1  1  1  1 X+2  0 X+2  1  2  2  1  1  1  1
 0  1  0  0  1 X+1  1 X+2  3  1  X  3 X+2  1 X+3  1  0 X+3  1  0  2  1  1 X+2  2  1  2 X+3  1  1  3  0 X+2 X+2  X  1 X+3 X+2  0  1  1  X  2  1  1 X+1  0  3  X  3  0  1  2 X+1  X  1  X X+3  3  0
 0  0  1  1  1  0  1  3  1  1  1  0  2  X  1  0 X+2 X+2 X+1  1 X+3  0  1  3  1  1  2  2 X+2  2  X X+3  1  2  1 X+2  X  1 X+2  1 X+3  1 X+2 X+2 X+2  X  X  1 X+3  0  1  1  1  3  1  3 X+2 X+1  3  0
 0  0  0  X  0  0  2  2 X+2  X  X X+2  X X+2 X+2  0  2  0  0  0  X X+2  2  2  X  X X+2  0  X  2  0  X  2  0 X+2 X+2  X  X X+2  0  X  2  2  0  X  2 X+2  X X+2  X  0 X+2 X+2  X  X  0  0  0  2  0
 0  0  0  0  X  2  X X+2  2  2 X+2  X  X X+2 X+2 X+2  X  X  0  X  X  0  0  2  2  0  0  X  2 X+2  2  2  0  0  X X+2 X+2  2 X+2  2  0  X X+2  0  0  0  2 X+2  0  X  X X+2 X+2 X+2  0  0  0 X+2 X+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+53x^52+126x^53+399x^54+450x^55+666x^56+632x^57+742x^58+628x^59+928x^60+674x^61+803x^62+530x^63+535x^64+322x^65+365x^66+144x^67+73x^68+58x^69+18x^70+8x^71+14x^72+10x^73+9x^74+2x^76+2x^77

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 2.91 seconds.