The generator matrix

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

generates a code of length 43 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+30x^41+63x^42+72x^43+60x^44+22x^45+1x^46+4x^47+2x^56+1x^60

The gray image is a code over GF(2) with n=172, k=8 and d=82.
This code was found by Heurico 1.16 in 0.0258 seconds.