The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+300x^10+1586x^11+5784x^12+14968x^13+20128x^14+15244x^15+5707x^16+1464x^17+324x^18+18x^19+12x^20

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 4.73 seconds.