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 2 X 2 X X X X X 1
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 X X X X 0 2 0 0 2 0
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 0 0 2 2 2 0 0 0 2
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 0 2 0 2 2
generates a code of length 44 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 42.
Homogenous weight enumerator: w(x)=1x^0+11x^42+12x^43+76x^44+16x^45+4x^46+3x^48+4x^51+1x^58
The gray image is a code over GF(2) with n=176, k=7 and d=84.
This code was found by Heurico 1.16 in 0.0351 seconds.