The generator matrix

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

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+10x^10+33x^12+430x^14+26x^16+6x^18+3x^20+2x^22+1x^24

The gray image is a code over GF(2) with n=112, k=9 and d=40.
This code was found by Heurico 1.16 in 0.015 seconds.