The generator matrix

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

generates a code of length 14 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+66x^10+420x^11+1459x^12+3392x^13+5692x^14+3488x^15+1377x^16+368x^17+106x^18+12x^19+3x^20

The gray image is a code over GF(2) with n=112, k=14 and d=40.
This code was found by Heurico 1.16 in 0.359 seconds.