The generator matrix

 1  0  0  0  1  1  1 2X+2  1 3X+2  1  1 3X  1
 0  1  0  0 2X+2 2X+1  3  1 3X+2  1 X+1 2X+2  1 2X+3
 0  0  1  0 2X+3  1 2X+2 2X+3  0  1  X 3X+3 3X X+1
 0  0  0  1  1 2X+2 2X+3 3X+3 X+1  X  X 3X+2  1 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+276x^10+1662x^11+5650x^12+15184x^13+19906x^14+15356x^15+5623x^16+1568x^17+280x^18+22x^19+6x^20+2x^22

The gray image is a code over GF(2) with n=112, k=16 and d=40.
This code was found by Heurico 1.16 in 4.98 seconds.