The generator matrix

 1  0  0  1  1  1 X+2  1  1  X  1  1  1  1
 0  1  0  X X^2+1 X^2+X+1  1 X^2+X X^2+3  1 X^2+X+3 X+1 X^2 X^2
 0  0  1  1 X+1  X X^2+1 X^2+X+3 X^2+3 X+3 X^2+2 X+1  1 X^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+88x^11+432x^12+798x^13+1493x^14+784x^15+382x^16+86x^17+27x^18+4x^19+1x^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 0.016 seconds.