The generator matrix

 1  1  1  1  1  1  1  X 2X  1  X  X  2  X  X  X
 0  X  0 X+2  2 3X+2 2X+2 3X+2  X 3X+2 X+2 3X  2  2  2 2X+2
 0  0 2X+2  0  2  2 2X 2X+2  2  2  0 2X  2  2 2X  0
 0  0  0 2X  0  0 2X 2X  0  0 2X 2X 2X  0  0  0
 0  0  0  0 2X  0  0  0 2X 2X 2X 2X 2X  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+74x^12+16x^13+360x^14+240x^15+683x^16+240x^17+336x^18+16x^19+70x^20+8x^22+4x^24

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 0.015 seconds.