The generator matrix

 1  1  1  1  1  1  1  1  1  1  X  X  2  X  X  X
 0 2X+2  0  2  0 2X 2X+2 2X+2  0 2X 2X  0  0  2  2  0
 0  0 2X+2  2  0  2  2 2X  0  2  2 2X+2 2X+2  2 2X+2  0
 0  0  0 2X  0  0 2X  0 2X 2X  0  0 2X  0 2X  0
 0  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X  0  0  0  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+40x^12+8x^13+108x^14+184x^15+347x^16+184x^17+96x^18+8x^19+44x^20+4x^22

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 -6.48e-008 seconds.