The generator matrix

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

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+168x^34+12x^35+315x^36+96x^37+468x^38+236x^39+635x^40+320x^41+590x^42+260x^43+437x^44+96x^45+250x^46+4x^47+129x^48+58x^50+15x^52+2x^54+3x^56+1x^60

The gray image is a code over GF(2) with n=164, k=12 and d=68.
This code was found by Heurico 1.16 in 1.42 seconds.