The generator matrix

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

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+45x^12+32x^14+873x^16+32x^18+34x^20+6x^24+1x^28

The gray image is a code over GF(2) with n=128, k=10 and d=48.
This code was found by Heurico 1.16 in -1.01e-007 seconds.