The generator matrix

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

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+51x^34+168x^35+443x^36+464x^37+798x^38+826x^39+1024x^40+778x^41+1101x^42+690x^43+703x^44+470x^45+334x^46+144x^47+125x^48+30x^49+18x^50+10x^51+8x^52+2x^53+2x^54+2x^55

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 1.87 seconds.