The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 0 X 0 X X X 2 X 2 1 1 X 0 X 0 1 1 X X 2 X 2 1 X X X
0 X 0 X+2 0 X+2 0 X 2 X+2 2 X 2 X+2 2 X X+2 X X+2 X 0 2 X X X X 0 0 X+2 X X+2 X 2 2 0 X X X X 0 0 2 2
0 0 2 0 0 2 2 2 2 0 2 0 0 2 0 2 0 0 2 2 2 2 2 2 0 0 0 0 0 2 2 0 0 0 2 2 2 0 0 2 0 2 0
0 0 0 2 2 2 2 0 0 0 2 2 2 0 0 2 0 2 2 0 2 2 2 0 0 2 0 2 2 2 0 0 2 0 0 0 2 2 0 2 2 0 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+12x^41+11x^42+80x^43+12x^44+4x^46+3x^48+4x^49+1x^58
The gray image is a code over GF(2) with n=172, k=7 and d=82.
This code was found by Heurico 1.16 in 0.0322 seconds.