The generator matrix

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

generates a code of length 14 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 11.

Homogenous weight enumerator: w(x)=1x^0+120x^11+336x^12+1108x^13+1008x^14+1084x^15+299x^16+108x^17+16x^18+12x^19+4x^20

The gray image is a code over GF(2) with n=112, k=12 and d=44.
This code was found by Heurico 1.16 in 0.031 seconds.