The generator matrix

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

generates a code of length 24 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+195x^20+108x^21+280x^22+296x^23+352x^24+240x^25+284x^26+120x^27+128x^28+4x^29+24x^30+11x^32+4x^34+1x^36

The gray image is a code over GF(2) with n=96, k=11 and d=40.
This code was found by Heurico 1.16 in 1.42 seconds.