The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  1  1  1  1  1  0  X  X  0  1  1  1  1  0  X  X  1  1  1  2  1  2  2  2  1  1  1  X
 0  X  0  X  0  0  X X+2  0  2 X+2  X  0  X  X  0  2  2 X+2  X  0  0  X  2  2  X  0 X+2 X+2  2  2  0  X X+2  X  0  2  2  0  2  2 X+2 X+2  X  0  X X+2  2  X  X  0  X X+2  X  X  X X+2 X+2  2 X+2
 0  0  X  X  0 X+2  X  0  2  X  0  X  0 X+2  2 X+2  X  X  2  0  2  0 X+2  2  2 X+2  X  X X+2  X  X X+2  X  0  0  2  2  X X+2 X+2  X  X  0 X+2  X  2  2  X  2  2  X  X  X  X X+2  X  X X+2 X+2  0
 0  0  0  2  0  0  0  0  2  2  2  0  2  0  2  0  0  0  2  0  2  2  2  0  0  2  0  0  2  2  2  0  2  0  0  0  0  2  2  0  2  0  2  0  2  0  2  2  0  0  0  0  0  2  2  0  0  2  2  0
 0  0  0  0  2  0  0  0  0  0  0  0  2  0  0  0  2  2  2  2  0  2  0  2  0  2  2  2  0  2  0  2  2  2  0  0  2  2  2  0  0  0  0  0  0  2  2  2  2  2  0  2  0  2  2  0  0  2  2  0
 0  0  0  0  0  2  0  0  0  2  0  2  2  2  2  2  2  0  2  0  0  0  2  2  0  2  2  0  0  2  0  0  0  0  2  0  2  0  2  2  2  2  2  0  0  0  2  0  0  2  0  0  0  0  0  0  2  2  2  0
 0  0  0  0  0  0  2  0  2  2  2  2  2  2  2  0  0  0  2  0  2  2  0  0  0  0  0  2  0  2  2  0  2  2  2  2  2  0  0  2  0  0  0  0  0  0  2  0  2  2  2  0  0  2  0  0  0  0  0  2
 0  0  0  0  0  0  0  2  0  0  0  2  0  0  2  2  2  2  0  2  2  0  2  0  2  2  0  0  2  2  0  2  0  0  0  0  0  2  2  0  2  0  2  2  0  2  2  0  2  0  0  2  2  0  0  0  2  0  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+204x^52+12x^53+184x^54+80x^55+412x^56+184x^57+444x^58+240x^59+648x^60+240x^61+462x^62+176x^63+342x^64+72x^65+150x^66+16x^67+144x^68+4x^69+34x^70+32x^72+6x^74+3x^76+5x^80+1x^92

The gray image is a code over GF(2) with n=240, k=12 and d=104.
This code was found by Heurico 1.16 in 65.4 seconds.