The generator matrix

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

generates a code of length 14 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+100x^12+64x^13+200x^14+64x^15+67x^16+8x^18+8x^20

The gray image is a code over GF(2) with n=112, k=9 and d=48.
This code was found by Heurico 1.16 in 0.438 seconds.