The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 X 1 1 1 1 1 1
0 2X 0 0 0 0 0 2X 0 0 0 0 2X 2X 0 2X 2X 2X 2X 2X 2X 0 0 0
0 0 2X 0 0 0 0 2X 0 0 2X 2X 2X 2X 2X 0 0 2X 0 2X 0 0 0 2X
0 0 0 2X 0 0 0 2X 0 2X 2X 0 0 0 2X 0 2X 2X 2X 2X 2X 0 2X 2X
0 0 0 0 2X 0 0 2X 0 2X 0 2X 0 2X 2X 2X 0 0 0 2X 2X 2X 2X 2X
0 0 0 0 0 2X 0 2X 2X 0 0 2X 0 2X 0 0 0 2X 2X 0 2X 2X 2X 0
0 0 0 0 0 0 2X 2X 2X 0 2X 0 0 2X 2X 2X 0 0 2X 2X 0 0 2X 0
generates a code of length 24 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 20.
Homogenous weight enumerator: w(x)=1x^0+50x^20+32x^22+872x^24+32x^26+21x^28+15x^32+1x^44
The gray image is a code over GF(2) with n=192, k=10 and d=80.
This code was found by Heurico 1.16 in 3.01 seconds.