The generator matrix

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

generates a code of length 41 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+40x^39+32x^40+120x^41+24x^42+24x^43+4x^44+8x^45+1x^48+1x^52+1x^60

The gray image is a code over GF(2) with n=164, k=8 and d=78.
This code was found by Heurico 1.13 in 0.016 seconds.