The generator matrix

 1  0  0  1  1  1  2  1  1  2  1  1  0  0  X X+2  1  1  X  1  1 X+2 X+2  0  X  1  1  0  1  X  1  2  1  1  1  1 X+2  2  X  1  1  0  1
 0  1  0  2  3  1  1  0  3  1  2  1  1 X+2  X  0  X X+3  1 X+2 X+1  1 X+2  X  0  2  1  1 X+2  1  0  1  1  X  3 X+3  2  0  1 X+2 X+1  1  X
 0  0  1 X+3 X+1  2 X+1 X+2  3  3  1  X X+2  1  1  1  1  X  X X+1  0  2  1  1  1 X+1  0  2  3  2  1  X X+2 X+1 X+2  0  1  1  1  1  X X+1  X

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+66x^40+82x^41+127x^42+58x^43+59x^44+22x^45+32x^46+30x^47+25x^48+9x^50+1x^68

The gray image is a code over GF(2) with n=172, k=9 and d=80.
This code was found by Heurico 1.13 in 0.016 seconds.