The generator matrix

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

generates a code of length 41 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 43.

Homogenous weight enumerator: w(x)=1x^0+8x^43+5x^44+2x^46

The gray image is a code over GF(2) with n=164, k=4 and d=86.
This code was found by Heurico 1.16 in 0.0194 seconds.