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

generates a code of length 43 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+114x^40+120x^42+228x^44+8x^46+36x^48+4x^52+1x^80

The gray image is a code over GF(2) with n=172, k=9 and d=80.
This code was found by Heurico 1.16 in 0.0548 seconds.