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.