The generator matrix

 1  0  1  1  1 X+2  1  1  0  1  1 X+2  1  1  0  1  1 X+2  1  1  2  1  1  X  1  1  X  1  1  1  1  1  1  1  1  0  1  1 X+2  X  X  1  1
 0  1 X+1 X+2  1  1 X+1  0  1 X+2  3  1  0 X+1  1 X+2  3  1  2 X+3  1  X  3  1  0 X+2  0 X+2  2  X  2  X  2  2 X+1  1 X+2  3  1  2 X+2 X+3  3
 0  0  2  0  0  0  0  2  2  2  2  2  0  0  0  0  0  0  2  2  2  2  2  2  0  2  2  2  2  2  0  0  2  0  0  0  0  2  2  0  2  0  0
 0  0  0  2  0  2  2  2  2  0  2  0  2  0  2  0  2  0  0  2  0  2  0  2  0  2  0  2  0  0  2  0  2  2  0  0  2  0  0  0  2  2  0
 0  0  0  0  2  0  2  2  2  2  0  2  0  2  0  0  2  0  2  0  2  2  0  2  2  2  0  0  0  2  2  0  0  0  0  2  2  2  0  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+128x^40+158x^42+102x^44+92x^46+21x^48+6x^50+1x^52+1x^56+1x^60+1x^64

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 0.0338 seconds.