The generator matrix

 1  0  1  1  1  0  1  1  0  1  X  1  1  1 X+2  1  X  1  1  1 X+2  1  1  1 X+2  0  1  1  1 X+2  1  1  0 X+2  1  1  X  1  1  1  0  X  1
 0  1  1  0  1  1  2 X+1  1 X+2  1  1  1  2  1 X+1  1  2  3  2  1  3  0 X+2  1  1  3 X+1  3  1  X  2  1  1 X+1  1 X+2  0 X+2 X+1  1  1  0
 0  0  X  0  0  0  0  0  0  0  0  2  X X+2 X+2  X  X  X  X  X  X  2  X X+2  X  X X+2  2 X+2  X  X  2  0  0  X X+2  X X+2  2  X  0  2  2
 0  0  0  X  0  0  0  0  X X+2 X+2 X+2  X  X  0 X+2  X  2  2 X+2  0 X+2  0  X  X  2 X+2  2  0 X+2  0  0  2 X+2  X  0  X  2  X  2  0  X  0
 0  0  0  0  X  0  2 X+2  0  2  0  X  2 X+2 X+2  2 X+2  X  0 X+2  X  X X+2 X+2 X+2  X  2  2 X+2  2  2 X+2  X X+2  X  X  0  0 X+2 X+2  X  2  2
 0  0  0  0  0  X X+2 X+2 X+2  X  2  X  X  2  0  0  2  X  X X+2 X+2 X+2  0  0 X+2  2  2  0 X+2  0  2  0 X+2  X X+2  2  X X+2  X  2 X+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+44x^34+108x^35+247x^36+414x^37+600x^38+930x^39+1282x^40+1576x^41+1892x^42+2152x^43+2012x^44+1640x^45+1250x^46+848x^47+580x^48+368x^49+196x^50+116x^51+60x^52+34x^53+18x^54+6x^55+9x^56+1x^60

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 8.39 seconds.