The generator matrix

 1  1  1  1  1  1  1  1  1  1  X  X X^2  X  X  X
 0 X^2+2  0 X^2  0  2 X^2+2 X^2+2  0  2  2  0  0 X^2 X^2  0
 0  0 X^2+2 X^2  0 X^2 X^2  2  0 X^2 X^2 X^2+2 X^2+2 X^2 X^2+2  0
 0  0  0  2  0  0  2  0  2  2  0  0  2  0  2  0
 0  0  0  0  2  2  2  2  2  2  2  2  0  0  0  0

generates a code of length 16 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+40x^12+8x^13+108x^14+184x^15+347x^16+184x^17+96x^18+8x^19+44x^20+4x^22

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 0.015 seconds.