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  2  0  2  X  0  0  X  X  0  1  X  1  2  1  1  0  0  X  1
 0  X  0  0  0  X X+2  X  0  2  2  X X+2  X  X  0  2  0  X X+2  X  2  0 X+2  0  X  X X+2  X  0 X+2  X  X X+2  2  2  X  X  2  0  X X+2  0
 0  0  X  0  X  X X+2  0  0  0  X  X  X  0  2 X+2  2  2  0 X+2  0  X  X X+2  X X+2  X X+2 X+2  0  2  2  0  0  X  X  2  X X+2  X  2  2 X+2
 0  0  0  X  X  0 X+2  X  2  X  2  0  X  2 X+2  X  0  X X+2  X  2 X+2  0  0 X+2 X+2  2  X X+2  X  2 X+2  0  0  0  2  2 X+2 X+2  2  2  0 X+2
 0  0  0  0  2  0  0  0  2  2  2  2  2  0  0  2  2  0  0  0  2  2  0  0  2  2  2  0  2  2  0  0  2  0  0  0  0  2  0  0  2  0  0
 0  0  0  0  0  2  0  0  0  2  0  2  2  2  0  0  2  2  0  2  2  0  2  0  0  0  2  0  0  0  2  0  0  2  0  2  0  2  0  2  0  0  2
 0  0  0  0  0  0  2  0  2  0  0  2  2  2  0  0  0  0  2  2  2  2  2  0  2  2  0  2  0  0  0  0  0  2  0  0  0  0  2  2  0  2  0
 0  0  0  0  0  0  0  2  0  0  2  0  0  0  0  2  2  0  0  0  2  2  2  2  0  0  2  2  2  2  0  2  0  2  2  0  2  0  2  0  2  0  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+69x^34+104x^35+199x^36+238x^37+322x^38+476x^39+593x^40+778x^41+866x^42+912x^43+877x^44+804x^45+608x^46+464x^47+311x^48+196x^49+157x^50+88x^51+57x^52+30x^53+22x^54+4x^55+7x^56+2x^57+4x^58+3x^60

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 3.18 seconds.