The generator matrix

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

generates a code of length 12 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 7.

Homogenous weight enumerator: w(x)=1x^0+96x^7+799x^8+5120x^9+19488x^10+57248x^11+96640x^12+57248x^13+19488x^14+5120x^15+799x^16+96x^17+1x^24

The gray image is a code over GF(2) with n=96, k=18 and d=28.
This code was found by Heurico 1.16 in 42.3 seconds.