The generator matrix

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

generates a code of length 24 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 17.

Homogenous weight enumerator: w(x)=1x^0+86x^17+179x^18+338x^19+704x^20+1186x^21+1799x^22+2454x^23+2810x^24+2502x^25+1856x^26+1250x^27+678x^28+310x^29+128x^30+50x^31+29x^32+12x^33+5x^34+4x^35+2x^36+1x^38

The gray image is a code over GF(2) with n=96, k=14 and d=34.
This code was found by Heurico 1.16 in 3.65 seconds.