The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 1 2 1 X
0 2X+2 0 2 0 2X 2X+2 2X+2 0 2X 2 2X+2 0 0 2 0 2 2X+2 2X 2X 2X+2 0 2X
0 0 2X+2 2 0 2 2 2X 0 2 2 0 0 2 2X+2 2X+2 2 2 0 2X 2X 2X 2
0 0 0 2X 0 0 2X 0 2X 2X 0 2X 2X 2X 0 0 2X 0 0 2X 0 0 2X
0 0 0 0 2X 2X 2X 2X 2X 2X 0 2X 0 0 2X 2X 2X 0 2X 0 2X 0 0
generates a code of length 23 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 20.
Homogenous weight enumerator: w(x)=1x^0+121x^20+224x^22+256x^23+378x^24+43x^28+1x^40
The gray image is a code over GF(2) with n=184, k=10 and d=80.
This code was found by Heurico 1.16 in 47 seconds.