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  1  1  X  1  X  X  X  1  X  2  0  2  X  1  X  1
 0  X  0  0  0  0  0  0  2  2  X X+2  X  0  X X+2  X X+2  2  2  0  X  0  X  X  X  X  2  2  0 X+2  0 X+2  0  X  X  0  X  X  0  2  X  0
 0  0  X  0  0  0  0  0  0  0  0  0  2 X+2  X X+2 X+2 X+2 X+2  X X+2 X+2 X+2 X+2  2  2 X+2  X  X  2  2 X+2 X+2 X+2  0  2  2  2 X+2  X  2  0  0
 0  0  0  X  0  0  2 X+2  X  X  X  X  2 X+2  2  X  0  2 X+2  2 X+2  X  2 X+2 X+2 X+2  0  X  2 X+2  0  X  X  0  2  X  X  X  0  X  X  X  0
 0  0  0  0  X  0 X+2 X+2  X  2 X+2 X+2  0  X X+2 X+2  2  2  X  X  0  2  2  2  0 X+2  X  2 X+2  0  2  X  0 X+2  X X+2 X+2  0  0  0 X+2  2  X
 0  0  0  0  0  X  X  2 X+2  X X+2  2  X  X  2 X+2  2  X  0  0  2  2 X+2  X  X  0  X X+2 X+2 X+2  X  2  2  X  0 X+2  2 X+2 X+2  0  X  0  X

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+50x^34+92x^35+143x^36+256x^37+337x^38+418x^39+639x^40+770x^41+892x^42+1022x^43+947x^44+816x^45+566x^46+418x^47+278x^48+172x^49+149x^50+94x^51+70x^52+32x^53+21x^54+4x^55+2x^56+2x^57+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 3.17 seconds.