The generator matrix

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

generates a code of length 24 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+64x^16+86x^17+180x^18+250x^19+381x^20+626x^21+839x^22+1100x^23+1145x^24+1066x^25+867x^26+636x^27+403x^28+254x^29+149x^30+60x^31+50x^32+16x^33+13x^34+2x^35+4x^36

The gray image is a code over GF(2) with n=96, k=13 and d=32.
This code was found by Heurico 1.16 in 1.12 seconds.