The generator matrix

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

generates a code of length 59 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+257x^52+152x^53+690x^54+324x^55+1117x^56+340x^57+1158x^58+404x^59+1072x^60+404x^61+878x^62+268x^63+579x^64+124x^65+254x^66+28x^67+85x^68+4x^69+24x^70+22x^72+4x^74+2x^76+1x^88

The gray image is a code over GF(2) with n=236, k=13 and d=104.
This code was found by Heurico 1.16 in 3.32 seconds.