The generator matrix

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

generates a code of length 14 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+66x^10+432x^11+1363x^12+3648x^13+5372x^14+3704x^15+1281x^16+400x^17+106x^18+8x^19+3x^20

The gray image is a code over GF(2) with n=112, k=14 and d=40.
This code was found by Heurico 1.16 in 0.344 seconds.