The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  X  1  1  1  1  0  X
 0  X  0  X  0 2X 3X+2 2X+2 3X+2 2X+2 2X+2 3X X+2 2X+2  2 3X+2  X  2 2X  2  X 3X  X X+2
 0  0  X  X  2 X+2 3X+2  2 2X  0  X X+2 3X  X X+2  2 2X+2 3X+2 2X  2 3X+2 X+2  0 2X+2
 0  0  0 2X  0  0  0 2X 2X 2X 2X 2X  0  0 2X 2X  0  0 2X  0  0  0 2X  0
 0  0  0  0 2X 2X  0  0 2X 2X  0  0  0  0 2X 2X  0 2X 2X  0 2X  0  0 2X

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+154x^20+80x^21+620x^22+704x^23+1039x^24+672x^25+584x^26+64x^27+142x^28+16x^29+12x^30+7x^32+1x^40

The gray image is a code over GF(2) with n=192, k=12 and d=80.
This code was found by Heurico 1.16 in 0.172 seconds.