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

generates a code of length 41 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+318x^36+152x^38+684x^40+336x^42+380x^44+24x^46+130x^48+22x^52+1x^64

The gray image is a code over GF(2) with n=164, k=11 and d=72.
This code was found by Heurico 1.16 in 20.3 seconds.