The generator matrix

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

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+50x^11+284x^12+298x^13+846x^14+222x^15+265x^16+62x^17+10x^18+8x^19+2x^20

The gray image is a code over GF(2) with n=112, k=11 and d=44.
This code was found by Heurico 1.16 in -1.53e-008 seconds.