The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  X  1  1  1  1
 0 2X  0  0  0  0  0  0  0  0 2X 2X  0  0  0 2X 2X 2X 2X 2X  0  0  0  0
 0  0 2X  0  0  0  0  0  0 2X 2X 2X  0 2X 2X  0 2X 2X  0  0  0  0  0  0
 0  0  0 2X  0  0  0  0  0 2X  0 2X 2X 2X  0 2X  0 2X 2X  0  0  0  0  0
 0  0  0  0 2X  0  0  0 2X  0  0 2X 2X  0 2X 2X  0  0 2X 2X  0  0  0  0
 0  0  0  0  0 2X  0  0 2X  0 2X  0  0 2X 2X 2X  0 2X 2X  0  0  0  0  0
 0  0  0  0  0  0 2X  0 2X 2X 2X  0  0  0 2X 2X 2X  0  0 2X  0  0  0  0
 0  0  0  0  0  0  0 2X 2X 2X  0  0 2X 2X 2X  0 2X  0 2X  0  0  0  0  0

generates a code of length 24 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+78x^16+32x^20+1828x^24+32x^28+73x^32+4x^40

The gray image is a code over GF(2) with n=192, k=11 and d=64.
This code was found by Heurico 1.16 in 0.032 seconds.