The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 X X 2 X 2
0 2X+2 0 2X+2 0 2X+2 0 2X+2 0 2X+2 2X 2 2X 2 2X+2 2 2X 0 2X 2X+2 2X+2 2X+2
0 0 2X 0 0 0 2X 0 0 2X 2X 0 0 2X 2X 2X 0 0 2X 2X 0 2X
0 0 0 2X 0 0 0 2X 2X 2X 2X 2X 0 2X 0 2X 0 2X 2X 0 0 0
0 0 0 0 2X 2X 2X 2X 2X 0 2X 0 2X 0 0 2X 0 2X 0 0 0 2X
generates a code of length 22 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 20.
Homogenous weight enumerator: w(x)=1x^0+135x^20+256x^22+110x^24+8x^28+1x^32+1x^36
The gray image is a code over GF(2) with n=176, k=9 and d=80.
This code was found by Heurico 1.16 in 3.7 seconds.