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  0  1  X  1  1  X  1  1  0  1  2  1  2  1  1  1  2  0
 0  X  0  0  0  X X+2  X  2  2  X  0  0  X X+2 X+2  0  2  X  2  X  2  X  2  2  2  X X+2  X X+2  0  X  0  0 X+2  0  0 X+2  X  X  0
 0  0  X  0  X  X  X  0  2  0 X+2  X X+2  0 X+2  0  X  2  2 X+2  2  0  0  2  X  X  0 X+2  0  X  2  2  X  X X+2  X X+2  0  2  X  0
 0  0  0  X  X  0  X X+2  0  X  2  X  2 X+2  X  0 X+2  0  2  2  2  0 X+2  X X+2  0  X  2  X  X X+2  0  2 X+2  0  X X+2  X  X  0  X
 0  0  0  0  2  0  0  0  2  2  2  2  0  2  2  2  0  0  0  2  2  2  2  2  0  0  2  2  0  2  2  2  2  0  0  0  2  0  2  2  0
 0  0  0  0  0  2  0  2  0  0  0  2  2  0  2  0  0  2  2  0  2  2  2  2  2  0  2  2  0  0  0  0  0  2  0  2  2  0  2  2  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+340x^36+120x^38+668x^40+368x^42+376x^44+24x^46+130x^48+20x^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 40.7 seconds.