The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 2X 2X  X  1
 0  X 2X+2 X+2  0 X+2 2X+2 3X  0 X+2 2X+2 3X  0 X+2 2X 3X+2 2X+2  2 3X 3X 2X 2X 2X  0
 0  0 2X  0  0  0 2X 2X 2X  0  0 2X  0 2X 2X 2X  0 2X  0 2X 2X  0  0 2X
 0  0  0 2X  0  0 2X 2X  0 2X 2X 2X 2X  0 2X  0  0  0 2X  0  0 2X  0 2X
 0  0  0  0 2X 2X  0  0 2X 2X 2X 2X  0 2X 2X  0  0 2X 2X 2X  0  0 2X 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+12x^20+62x^21+207x^22+90x^23+351x^24+48x^25+169x^26+32x^27+18x^28+18x^29+7x^30+6x^31+2x^32+1x^42

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.