The generator matrix

 1  0  1  1  1  0  1  1  0  1  2  1  1  1  X  X  1  1 X+2  1  1  1  1 X+2  1  1  X  2  1  1  0  1  1  1  1  1  X  1  X  2  1  1  X
 0  1  1  0 X+1  1 X+3  0  1  3  1  2 X+3 X+2  1  1  1 X+2  1 X+3  X  3  0  1  3 X+2  1  1  0  X  1  2  1 X+3 X+3  2 X+2 X+2  1  1  1  X X+2
 0  0  X  0  0  0  0  X  X X+2  X  X  2  X X+2  0  0  2  X X+2  X  2  2  0  X  X  0 X+2  X  0  0 X+2  X  X  2 X+2  2  2 X+2 X+2  2  X  0
 0  0  0  X  0 X+2 X+2  X  X  X  0  2  2 X+2  2 X+2  X  0  X  2  2  2  2  2  0  X  0  0  X X+2  2  0  2  2  X  0 X+2  X  0  2 X+2  X  0
 0  0  0  0  2  0  0  0  0  0  0  2  0  2  0  2  2  2  2  0  2  2  2  2  0  0  2  2  0  2  0  0  0  2  2  2  0  2  0  0  2  0  2
 0  0  0  0  0  2  0  0  0  2  2  0  2  0  0  2  2  2  2  0  0  2  0  0  2  2  2  0  0  2  2  2  2  0  2  0  2  0  2  2  0  0  2
 0  0  0  0  0  0  2  0  2  0  2  0  2  0  2  2  0  2  2  2  2  2  0  0  2  0  0  2  2  2  0  0  2  2  0  0  2  2  0  2  0  0  2
 0  0  0  0  0  0  0  2  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  2  2  0  2  0  0  0  2  2  0  0  2  2  2  0  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+109x^34+12x^35+423x^36+184x^37+814x^38+672x^39+1569x^40+1352x^41+2206x^42+1704x^43+2186x^44+1352x^45+1633x^46+672x^47+843x^48+184x^49+310x^50+12x^51+87x^52+40x^54+11x^56+6x^58+1x^62+1x^66

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 8.42 seconds.