The generator matrix

 1  0  0  1  1  1  0  1 X+2  X  1 3X  1 3X  1  1 2X+2 2X  1 X+2  X X+2  1  1
 0  1  0  X 2X+1 X+3  1 2X+2  1 X+2  3  1 2X+2  1 X+1 3X+2  1  1  0  2  1  1 2X+3  2
 0  0  1  1  1  X X+3 2X+1 2X  1 X+1  3  X  X 2X X+3 3X 3X+1 X+1  1 2X+1  2 2X+3 2X+2
 0  0  0  2 2X+2 2X  2  2  0 2X+2 2X 2X 2X+2  2 2X+2  0  0 2X 2X+2 2X+2  0 2X+2  2  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+255x^20+980x^21+1794x^22+3428x^23+3522x^24+3512x^25+1688x^26+856x^27+255x^28+52x^29+30x^30+4x^31+7x^32

The gray image is a code over GF(2) with n=192, k=14 and d=80.
This code was found by Heurico 1.16 in 0.781 seconds.