The generator matrix

 1  0  0  1  1  1  0  1  X  1  X  1  1  X  1  1 X+2  1  1  1 X+2  1  1  1
 0  1  0  0  1  1  1 X+1 X+2  X  1 X+1 X+2  1  1 X+3  X  X  2  2  1  3 X+3  0
 0  0  1  1  0 X+1  1  2  1  0 X+1 X+1  3  X  2 X+2  1 X+2  0 X+1 X+3  X  X X+1
 0  0  0  X  2 X+2  X  2  X  X  0  0  0 X+2  X  2 X+2 X+2 X+2  X  X  X  X  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+109x^20+198x^21+325x^22+288x^23+311x^24+238x^25+280x^26+120x^27+111x^28+42x^29+9x^30+8x^31+4x^32+2x^33+2x^34

The gray image is a code over GF(2) with n=96, k=11 and d=40.
This code was found by Heurico 1.11 in 0.0244 seconds.