The generator matrix

 1  0  1  1  1 X+2  1  1 2X+2  1  1 3X  1  1  0  1  1  1  1  1  1  X  X  1
 0  1 X+1 X+2  3  1 2X+2 3X+3  1 3X 2X+1  1  0 X+1  1 X+2 2X+2 X+2 2X+2 3X  0 3X 3X X+1
 0  0 2X  0  0 2X 2X  0  0 2X 2X 2X  0  0 2X  0 2X 2X  0  0 2X  0 2X  0
 0  0  0 2X  0 2X 2X 2X 2X  0 2X  0 2X  0 2X  0  0 2X  0 2X  0  0 2X  0
 0  0  0  0 2X 2X 2X 2X  0 2X  0 2X  0 2X 2X  0  0 2X 2X 2X 2X 2X  0  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+19x^20+136x^21+168x^22+600x^23+211x^24+600x^25+149x^26+136x^27+23x^28+2x^30+1x^32+1x^34+1x^40

The gray image is a code over GF(2) with n=192, k=11 and d=80.
This code was found by Heurico 1.16 in 0.031 seconds.