The generator matrix

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

generates a code of length 41 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+28x^42+2x^44+1x^48

The gray image is a code over GF(2) with n=164, k=5 and d=84.
This code was found by Heurico 1.16 in 0.0196 seconds.