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

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+122x^36+120x^38+288x^40+240x^42+180x^44+24x^46+39x^48+9x^52+1x^68

The gray image is a code over GF(2) with n=164, k=10 and d=72.
This code was found by Heurico 1.16 in 84.7 seconds.