The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  X  X  X  X  X  X  X  X  0  1
 0 X^2+2  0 X^2  0  0 X^2 X^2+2  2  2 X^2+2 X^2  2  2 X^2+2 X^2  2 X^2 X^2+2  0 X^2+2 X^2+2  2 X^2 X^2  0  0  0 X^2
 0  0 X^2+2 X^2  2 X^2 X^2+2  2  2 X^2 X^2+2  2  0 X^2+2 X^2  0 X^2 X^2  0 X^2+2 X^2  2 X^2+2 X^2+2  2  0  2 X^2 X^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+22x^27+63x^28+92x^29+53x^30+12x^31+8x^32+3x^34+2x^39

The gray image is a code over GF(2) with n=232, k=8 and d=108.
This code was found by Heurico 1.16 in 0.016 seconds.