The generator matrix

 1  0  1  1  1 X^2+X+2  1  1  1  1  1  1  2  1
 0  1 X+1 X^2+X+2 X^2+1  1  0 X+1  X  2 X+1 X+2  X  2
 0  0 X^2  0 X^2+2  2 X^2  0 X^2+2 X^2  2  0 X^2  0
 0  0  0 X^2+2 X^2+2 X^2+2 X^2  2  0  2  0  0  2 X^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+31x^10+104x^11+342x^12+800x^13+1563x^14+784x^15+327x^16+96x^17+37x^18+8x^19+2x^20+1x^22

The gray image is a code over GF(2) with n=112, k=12 and d=40.
This code was found by Heurico 1.16 in 0.032 seconds.