The generator matrix

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

generates a code of length 14 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 9.

Homogenous weight enumerator: w(x)=1x^0+242x^9+1162x^10+6214x^11+22149x^12+60202x^13+81937x^14+60676x^15+22077x^16+6062x^17+1156x^18+230x^19+29x^20+6x^21+1x^22

The gray image is a code over GF(2) with n=112, k=18 and d=36.
This code was found by Heurico 1.16 in 62.1 seconds.