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  X  0  1  1  1  1  1  1  1  1  X  1  1  1  1  0  2  X  1  0  1  X  0  1  1  X  1  X  0  X  X  1
 0  X  0 X+2  0 X+2  0 X+2  2 X+2  0 X+2  0  X X+2  0  2 X+2  0 X+2  0 X+2  2 X+2  0  X  2  X X+2  X  X  2 X+2 X+2  2  2  X  2 X+2  2  0  2  2  X  2 X+2 X+2  X  0 X+2  X  X  2 X+2  X  X  X X+2 X+2  0
 0  0  2  0  0  0  0  0  2  0  0  2  2  2  2  0  2  0  0  0  2  0  2  2  2  0  0  0  2  0  2  0  0  0  2  0  0  2  0  0  2  2  2  0  2  0  2  2  0  0  2  0  2  2  2  2  0  0  2  0
 0  0  0  2  0  0  0  0  0  0  2  2  2  0  2  0  2  2  2  0  0  2  0  2  2  0  2  2  0  0  0  2  0  0  2  2  0  2  0  0  0  0  2  2  2  2  0  2  0  2  2  2  0  0  0  2  2  0  0  0
 0  0  0  0  2  0  0  0  0  0  2  0  0  0  0  2  2  0  2  2  2  2  0  0  2  2  2  2  2  0  0  0  2  0  0  0  2  0  2  0  2  0  2  2  0  0  2  0  2  0  2  2  2  0  2  2  2  0  0  0
 0  0  0  0  0  2  0  0  0  2  0  0  0  2  2  0  0  2  2  0  2  0  2  2  2  2  2  0  2  0  0  0  2  2  0  0  0  2  2  2  2  2  2  2  2  2  2  0  2  2  0  0  0  0  2  0  2  2  2  0
 0  0  0  0  0  0  2  0  2  0  2  0  0  0  2  2  0  2  0  2  0  2  2  0  2  0  2  2  2  2  2  0  2  2  0  0  0  2  0  0  0  0  0  2  2  2  0  2  2  2  0  0  0  2  2  2  0  0  0  2
 0  0  0  0  0  0  0  2  0  2  2  2  2  2  2  2  0  2  2  2  2  2  0  0  2  2  0  0  0  0  2  2  2  0  0  0  0  2  0  2  0  0  0  0  0  2  2  0  2  0  2  0  0  0  0  2  0  0  0  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+55x^52+8x^53+147x^54+48x^55+202x^56+72x^57+244x^58+112x^59+277x^60+152x^61+263x^62+80x^63+163x^64+24x^65+84x^66+16x^67+55x^68+21x^70+10x^72+8x^74+4x^76+1x^78+1x^92

The gray image is a code over GF(2) with n=240, k=11 and d=104.
This code was found by Heurico 1.16 in 0.439 seconds.