The generator matrix

 1  0  0  1  1  1  2  0  1  1  2  0  1  1  X X+2  1  0  1  1  1  2  1  0 X+2  X  1 X+2  1 X+2  1  0  1 X+2  2  X  X  X  1  1  0  2  1
 0  1  0  0  3  3  1 X+2  2  1  1  1  2  1  X  2  2  1  3  1  0  1  2  X  1  0 X+3  X X+2  1  X  1  1  1  X  1  1  1  3 X+3  1 X+2  2
 0  0  1 X+1 X+3  2 X+3  1  X  3  1  X  1 X+2  1  1 X+3  2  1  0 X+2  1  2  1  1  1 X+1  1  0 X+2  3 X+2 X+1 X+2 X+2  0 X+3  0  3  X  1  1 X+2
 0  0  0  2  2  0  2  2  2  0  0  2  0  2  0  2  0  2  2  2  0  2  2  0  0  0  0  2  0  2  2  0  0  0  2  0  2  2  0  0  2  0  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+306x^40+296x^42+211x^44+88x^46+64x^48+32x^50+25x^52+1x^56

The gray image is a code over GF(2) with n=172, k=10 and d=80.
This code was found by Heurico 1.16 in 7.95 seconds.