The generator matrix

 1  0  0  1  1  1 X^2+X+2  0  1 X^2+X  1  1  1 X^2+2  1  1  1
 0  1  0  1  X X^2+X+1  1  1 X^2  1  2 X^2+1 X+1  0 X+1 X^2+1 X+2
 0  0  1  1  1  0  1  2 X+1 X+3 X^2 X+2 X^2+3  1 X^2+X X^2+X X+1
 0  0  0  X  2 X+2 X^2+X  X  X  0 X^2+X+2 X^2+2 X^2+2  X X^2+X+2 X+2 X^2+X

generates a code of length 17 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+276x^13+1138x^14+3234x^15+6955x^16+9392x^17+7292x^18+3190x^19+948x^20+284x^21+50x^22+6x^23+2x^27

The gray image is a code over GF(2) with n=136, k=15 and d=52.
This code was found by Heurico 1.16 in 1.75 seconds.