The generator matrix

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

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+200x^36+352x^37+534x^38+432x^39+478x^40+316x^41+452x^42+368x^43+380x^44+232x^45+166x^46+64x^47+73x^48+28x^49+16x^50+4x^52

The gray image is a code over GF(2) with n=164, k=12 and d=72.
This code was found by Heurico 1.16 in 0.399 seconds.