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+2X+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 3.05 seconds.