The generator matrix

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

generates a code of length 16 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+93x^12+320x^14+1225x^16+320x^18+82x^20+6x^24+1x^28

The gray image is a code over GF(2) with n=128, k=11 and d=48.
This code was found by Heurico 1.16 in 2.13 seconds.