The generator matrix

 1  0  1  1  1  0  1  1  2  1  1  0  1 X+2  1  1  1  1  1 X+2  X  1  1  0  1  1  2  1 X+2  1  1  0  X  1  1 X+2  1  0  1  1  0 X+2  1
 0  1  1  0  1  1 X+1  2  1 X+1  0  1 X+3  1 X+2  1  3  X  X  1  1 X+3 X+1  1  X  X  1 X+1  1  2 X+3  1  1  X X+2  1 X+1  X  1 X+3  X  1  0
 0  0  X  0  0  0  0  X  X  X  X  X  X  X X+2  0  2  2  X  2 X+2  0 X+2  X X+2  0  2  2 X+2  0  X  2  X X+2  X  2  0 X+2  0  0  2  2  0
 0  0  0  X  0 X+2  X  X X+2  X  2  2  2  0  0  2  X X+2 X+2  2  X  0  X  2  X  0  0  2  2  0  0  0  X  0  0  X  2 X+2 X+2  X X+2  0  0
 0  0  0  0  X  0  X X+2 X+2  2  X X+2  0  X  X X+2  X  2  X  0  X X+2  2  X  X X+2  X  2  0 X+2  X  X  2  0  2  0  0 X+2 X+2  2  0  2  0
 0  0  0  0  0  2  0  0  0  0  0  0  2  2  2  2  2  2  0  2  2  0  0  0  2  2  0  0  0  0  0  2  2  0  0  2  2  0  0  2  2  2  0
 0  0  0  0  0  0  2  2  2  2  0  0  2  2  2  2  0  2  0  0  2  2  0  2  2  0  2  2  2  0  0  2  2  0  2  2  0  0  2  0  0  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+91x^34+104x^35+296x^36+332x^37+795x^38+716x^39+1541x^40+1198x^41+2402x^42+1538x^43+2367x^44+1128x^45+1643x^46+670x^47+702x^48+312x^49+292x^50+102x^51+77x^52+36x^53+22x^54+6x^55+8x^56+2x^57+3x^58

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 8.48 seconds.