The generator matrix

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

generates a code of length 41 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+176x^34+76x^35+386x^36+484x^37+745x^38+948x^39+750x^40+1084x^41+881x^42+948x^43+579x^44+476x^45+359x^46+76x^47+124x^48+4x^49+75x^50+15x^52+4x^54+1x^56

The gray image is a code over GF(2) with n=164, k=13 and d=68.
This code was found by Heurico 1.16 in 2.3 seconds.