The generator matrix

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

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+106x^10+990x^11+2546x^12+7668x^13+10084x^14+7820x^15+2487x^16+920x^17+130x^18+6x^19+6x^20+4x^21

The gray image is a code over GF(2) with n=112, k=15 and d=40.
This code was found by Heurico 1.16 in 1.39 seconds.