The generator matrix

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

generates a code of length 29 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+244x^27+228x^28+216x^29+110x^30+120x^31+43x^32+56x^33+4x^35+2x^38

The gray image is a code over GF(2) with n=232, k=10 and d=108.
This code was found by Heurico 1.16 in 8.06 seconds.