The generator matrix

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

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+82x^17+165x^18+202x^19+295x^20+440x^21+788x^22+1308x^23+1564x^24+1336x^25+861x^26+476x^27+285x^28+176x^29+103x^30+60x^31+30x^32+14x^33+2x^34+2x^35+1x^38+1x^40

The gray image is a code over GF(2) with n=96, k=13 and d=34.
This code was found by Heurico 1.16 in 1.62 seconds.