The generator matrix

 1  0  0  1  1  1  X  1  1  2  2  1  2  1 X+2  1  1 X+2  1  1  X  1  1  0  1  1  1  0  X  X  X  1  1  1  0  1  1  1  1 X+2  2  1  1
 0  1  0  X  1 X+3  1 X+2  0  X  1 X+1  1 X+1  0  1  3  1  3  3  1  2  2  1  0 X+3 X+2  0  1  1  1  2  3  X  2 X+3  3 X+3 X+3  1  1  3  0
 0  0  1  1 X+3 X+2  1 X+3 X+2  1  X X+1  1  0  1  X  3 X+1  0 X+1  X  1  X  1  3  1  0  1  X  1  X  X  1 X+3  1  X X+3 X+1  X  0 X+1 X+2  0
 0  0  0  2  0  0  0  0  2  2  0  0  0  2  2  0  0  2  2  2  2  0  0  2  0  2  0  2  2  2  2  2  2  2  2  2  0  0  0  2  0  0  0
 0  0  0  0  2  0  0  0  0  0  0  2  0  0  0  0  2  2  2  2  2  2  2  0  2  2  0  0  0  2  0  0  2  0  2  2  0  0  2  2  0  2  0
 0  0  0  0  0  2  0  0  0  0  0  0  0  2  0  2  0  2  2  0  0  2  2  0  2  2  2  2  2  2  2  2  2  2  0  0  0  2  2  2  2  0  0
 0  0  0  0  0  0  2  0  0  0  0  0  2  0  2  2  2  2  0  0  2  0  0  2  2  0  0  2  2  0  2  2  2  0  0  0  0  2  2  0  2  2  0
 0  0  0  0  0  0  0  2  2  2  2  2  2  0  0  2  2  0  0  2  0  2  0  2  0  0  0  0  2  0  0  0  2  0  2  0  0  2  2  2  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+21x^34+90x^35+236x^36+440x^37+616x^38+1048x^39+1079x^40+1882x^41+1593x^42+2298x^43+1672x^44+1890x^45+1170x^46+1086x^47+537x^48+366x^49+169x^50+84x^51+50x^52+30x^53+14x^54+2x^55+7x^56+1x^58+2x^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 6.95 seconds.