The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  X  1
 0  2  0  2  0  2 2X 2X+2  0 2X 2X  2  2 2X+2
 0  0 2X  0  0 2X 2X 2X 2X 2X  0 2X 2X 2X
 0  0  0 2X 2X 2X 2X  0 2X  0 2X  0  0  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+14x^12+32x^13+164x^14+32x^15+9x^16+3x^18+1x^26

The gray image is a code over GF(2) with n=112, k=8 and d=48.
This code was found by Heurico 1.16 in 0.015 seconds.