The generator matrix

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

generates a code of length 14 over Z4[X]/(X^2+2X+2) 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 0.047 seconds.