The generator matrix

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

generates a code of length 17 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+73x^14+192x^15+573x^16+384x^17+560x^18+192x^19+64x^20+6x^22+2x^24+1x^30

The gray image is a code over GF(2) with n=136, k=11 and d=56.
This code was found by Heurico 1.16 in 0.719 seconds.