The generator matrix

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

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+28x^10+38x^11+41x^12+92x^13+625x^14+88x^15+49x^16+36x^17+18x^18+2x^19+5x^20+1x^22

The gray image is a code over GF(2) with n=112, k=10 and d=40.
This code was found by Heurico 1.16 in -3.24e-008 seconds.