The generator matrix

 1  0  0  0  1  1  1  1  2  1  1  1  X X+2 X+2  1  1  2  1  X  1  1  1  1  0  0  1  1  0  1  0  X  2  1  1  1  0  1 X+2  X  1
 0  1  0  0  0  0  1  3  1  2 X+1  3  1  1  0 X+3 X+2  X  3  X X+3  X  1  2  1  0 X+1 X+1  1  X  0 X+2  1  2  X X+3  2  3  1  1  X
 0  0  1  0  0  1  1  2  3  3 X+1 X+2  X X+3  1 X+2  1  1 X+1  1  2 X+2  1 X+2 X+2  1  3  2 X+2 X+3 X+2 X+2  1  1 X+3  0  1  3 X+3  3 X+1
 0  0  0  1 X+1 X+3  2 X+3 X+3  X X+1 X+2  3  2 X+1  0  X X+3 X+2  0  3 X+1 X+3  0  2  X X+2  X X+2  3  1  1  3  2  X X+1  0  0  X  3  X
 0  0  0  0  2  0  0  0  0  0  0  0  0  0  0  2  2  2  2  0  2  0  2  0  2  2  2  0  0  2  2  2  2  0  2  2  2  2  2  2  0
 0  0  0  0  0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  2  2  0  2  0  2  0  2  0  0  2  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+171x^34+446x^35+760x^36+1014x^37+1518x^38+1434x^39+1900x^40+1822x^41+2030x^42+1654x^43+1390x^44+914x^45+688x^46+286x^47+195x^48+90x^49+39x^50+20x^51+10x^52+2x^54

The gray image is a code over GF(2) with n=164, k=14 and d=68.
This code was found by Heurico 1.16 in 6.21 seconds.