The generator matrix

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

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+85x^10+104x^11+435x^12+800x^13+1274x^14+784x^15+417x^16+96x^17+81x^18+8x^19+11x^20

The gray image is a code over GF(2) with n=112, k=12 and d=40.
This code was found by Heurico 1.16 in 0.078 seconds.