The generator matrix
1 0 0 1 1 1 X^2+X+2 2 1 1 2 1 1 1 1 1
0 1 0 1 X X^2+X+1 1 1 X X+2 1 X^2+X+3 3 X^2+1 X^2+1 0
0 0 1 1 1 0 1 X X+1 2 X^2+1 X^2+X+1 X^2 X^2+X+1 X^2+X+2 X^2
0 0 0 X 2 X+2 X^2+X X^2+X X X^2+X X^2 X^2 0 X^2+X+2 X X^2
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+207x^12+1168x^13+2807x^14+7452x^15+9361x^16+7752x^17+2742x^18+992x^19+239x^20+40x^21+3x^22+4x^23
The gray image is a code over GF(2) with n=128, k=15 and d=48.
This code was found by Heurico 1.16 in 1.59 seconds.