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  2  X  1  0  X  X  1  0  X  2  2  0  1  1  1  1
 0  X  0  0  0  0  0  0  0 X+2  X  X  X  0  X X+2  2 X+2  0  2  X  0  X  2  X  X  X  2  X X+2  X X+2  X  2  0  X  X  X  0  2  0  X  2
 0  0  X  0  0  0  X X+2  X  2  X X+2  0 X+2  0 X+2 X+2  X  2  X  2 X+2  2  2  0  X  0  X X+2 X+2  2 X+2  2  0  X  0  2  2  2 X+2  0  X  0
 0  0  0  X  0  X  X  X  0 X+2  2  X X+2  X X+2  2  2  X  2  2  2  0  0  2  2  2  X  0 X+2  2  2 X+2 X+2  X X+2 X+2  X  X  X  0  X  X  0
 0  0  0  0  X  X  0  X X+2  X  0  X  2 X+2  2  0 X+2  0 X+2  0  X X+2  2  2  X  X X+2 X+2 X+2  2  0  2  0  X  X  2  X  2  2  0  0 X+2 X+2
 0  0  0  0  0  2  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  0  2  0  2  2  2  2  2  0  2  0  0  0  2  0  0  2  2  2  2  2
 0  0  0  0  0  0  2  0  2  0  2  2  2  2  0  0  0  0  0  2  2  0  2  2  2  0  0  2  2  2  2  0  0  0  0  2  0  0  2  0  2  2  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+55x^34+100x^35+169x^36+228x^37+294x^38+466x^39+573x^40+772x^41+947x^42+982x^43+1012x^44+804x^45+530x^46+426x^47+293x^48+204x^49+140x^50+62x^51+59x^52+40x^53+16x^54+12x^55+5x^56+1x^58+1x^66

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 3.13 seconds.