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

generates a code of length 43 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+298x^34+539x^36+1005x^38+128x^39+1226x^40+1024x^41+3111x^42+1792x^43+2901x^44+1024x^45+1558x^46+128x^47+781x^48+604x^50+175x^52+77x^54+8x^56+3x^58+1x^76

The gray image is a code over GF(2) with n=172, k=14 and d=68.
This code was found by Heurico 1.16 in 49 seconds.