The generator matrix

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

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+45x^20+16x^21+48x^22+240x^23+333x^24+240x^25+48x^26+16x^27+26x^28+9x^32+1x^36+1x^40

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 0.015 seconds.