The generator matrix

 1  1  1  1  1  1  1  1  1  X  1  2  1  1  X  X
 0 2X+2  0  2  0  0  2  2 2X 2X  0 2X  2 2X+2  2 2X+2
 0  0 2X+2  2  0 2X+2 2X+2  0 2X  2  0  2  2 2X 2X+2  0
 0  0  0 2X  0  0 2X  0  0 2X 2X  0  0 2X 2X  0
 0  0  0  0 2X  0  0  0  0 2X 2X 2X  0  0 2X 2X
 0  0  0  0  0 2X 2X 2X 2X  0  0 2X 2X 2X  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+82x^12+16x^13+176x^14+368x^15+770x^16+368x^17+168x^18+16x^19+73x^20+8x^22+1x^24+1x^28

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.