The generator matrix

 1  1  1  1  1  1  X  1  1  0  1  1  1  1 2X  1
 0  X  2 3X+2  0 3X+2 3X+2  2 3X  X  0  0 3X+2 3X+2 2X  0
 0  0 2X  0  0  0 2X  0 2X 2X  0 2X  0 2X 2X  0
 0  0  0 2X  0  0 2X 2X  0 2X 2X  0  0 2X  0  0
 0  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X  0  0 2X  0

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

Homogenous weight enumerator: w(x)=1x^0+22x^12+52x^13+129x^14+176x^15+217x^16+264x^17+119x^18+16x^19+14x^20+4x^21+7x^22+2x^24+1x^26

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 0 seconds.