The generator matrix

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

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+128x^20+194x^21+265x^22+364x^23+249x^24+282x^25+251x^26+140x^27+110x^28+34x^29+19x^30+8x^31+2x^33+1x^34

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 0.0524 seconds.