The generator matrix

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

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+46x^20+102x^21+147x^22+168x^23+152x^24+158x^25+101x^26+56x^27+54x^28+26x^29+5x^30+3x^32+2x^33+3x^34

The gray image is a code over GF(2) with n=96, k=10 and d=40.
This code was found by Heurico 1.16 in 0.02 seconds.