The generator matrix

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

generates a code of length 16 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 11.

Homogenous weight enumerator: w(x)=1x^0+144x^11+974x^12+3746x^13+12376x^14+28538x^15+39299x^16+28868x^17+12480x^18+3508x^19+906x^20+218x^21+8x^22+2x^23+4x^24

The gray image is a code over GF(2) with n=128, k=17 and d=44.
This code was found by Heurico 1.16 in 20.1 seconds.