The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+16x^41+8x^42+2x^44+4x^46+1x^48

The gray image is a code over GF(2) with n=164, k=5 and d=82.
This code was found by Heurico 1.16 in 0.0194 seconds.