The generator matrix

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

generates a code of length 14 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 9.

Homogenous weight enumerator: w(x)=1x^0+150x^9+1249x^10+6038x^11+23161x^12+58738x^13+83180x^14+59108x^15+23373x^16+5794x^17+1105x^18+214x^19+25x^20+6x^21+2x^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 59.8 seconds.