The generator matrix

 1  0  1  1  1 3X+2  1  1  2  1  1  1  1  1  1  1
 0  1 X+1 3X+2 2X+3  1  2 X+3  1  0 3X 2X+1 X+1 X+3 X+1  0
 0  0 2X  0  0 2X 2X  0  0 2X  0 2X  0  0 2X  0
 0  0  0 2X  0 2X 2X 2X 2X  0  0  0  0 2X 2X  0
 0  0  0  0 2X 2X 2X 2X  0 2X 2X  0  0  0  0  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+18x^12+76x^13+112x^14+660x^15+315x^16+660x^17+110x^18+76x^19+18x^20+2x^26

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.