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

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+97x^34+4x^35+365x^36+48x^37+563x^38+208x^39+904x^40+464x^41+1187x^42+600x^43+1116x^44+464x^45+915x^46+208x^47+573x^48+48x^49+263x^50+4x^51+101x^52+41x^54+10x^56+5x^58+2x^60+1x^62

The gray image is a code over GF(2) with n=172, k=13 and d=68.
This code was found by Heurico 1.16 in 13.4 seconds.