The generator matrix

 1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1
 0  X  0 3X+2 2X X+2  0  X  2 3X+2 X+2 2X+2 3X  X  0  0
 0  0 2X+2  0 2X 2X+2 2X+2  2  2  2  0 2X  0 2X 2X  0
 0  0  0 2X+2 2X+2  2 2X+2 2X  0  0 2X 2X 2X+2  2  0 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+30x^12+82x^13+101x^14+300x^15+1015x^16+312x^17+104x^18+68x^19+26x^20+6x^21+2x^22+1x^30

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 0.016 seconds.