The generator matrix

 1  0  0  1  1  1 3X  1  1  2  1 3X+2  1  1
 0  1  0 2X+2  1 3X+1  1 3X  3  1  0  1  1 3X
 0  0  1 3X+3  1 2X+2 2X+3 2X+3  X X+1 3X+2 3X+2 3X+3 2X+1
 0  0  0 2X 2X 2X  0  0  0 2X 2X 2X  0 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+210x^11+880x^12+1458x^13+3128x^14+1452x^15+827x^16+204x^17+24x^18+2x^19+4x^20+2x^21

The gray image is a code over GF(2) with n=112, k=13 and d=44.
This code was found by Heurico 1.16 in 0.11 seconds.