The generator matrix

 1  0  0  1  1  1  X  1  1 X+2  1  X  1  X  1  1  X  X  0 X+2  1  1  2  1  1  1  1  1 X+2  0  2  1  X  X  1  1  1  0 X+2  1  1
 0  1  0  0  1 X+3  1  2  3  1 X+2  X X+3  1  X X+1  2  1  1  1  X  3  2  3  2 X+2  3  X  X  1  1 X+3  1  1 X+1  1  0  1  1  X  1
 0  0  1  1 X+1  0  1  1 X+3  X X+2  1  0 X+1  1 X+2  1  0  1 X+3 X+3 X+3  1  2 X+3  2 X+2  2  1  3  0  X  3  X  2  1  2  X X+1  3  1
 0  0  0  X  X X+2  2  2  2  X  X  X  2 X+2  2 X+2  2  0 X+2  0 X+2  X X+2 X+2  0  0  0 X+2  0  0 X+2  2  2  2  2  X X+2  2  0 X+2  0
 0  0  0  0  2  0  0  0  2  0  0  0  0  0  2  2  2  2  0  0  2  2  2  2  0  0  0  2  2  2  0  2  0  2  2  2  0  0  2  0  0
 0  0  0  0  0  2  2  0  0  0  0  0  2  2  2  0  2  2  0  0  2  2  0  2  2  2  0  0  2  0  2  2  0  0  0  2  2  0  0  0  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+71x^34+156x^35+474x^36+440x^37+840x^38+604x^39+1214x^40+692x^41+1166x^42+652x^43+818x^44+356x^45+400x^46+116x^47+111x^48+44x^49+19x^50+8x^51+4x^52+4x^53+2x^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 1.89 seconds.