The generator matrix

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

generates a code of length 29 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+3x^28+44x^29+3x^30+12x^31+1x^34

The gray image is a code over GF(2) with n=232, k=6 and d=112.
This code was found by Heurico 1.16 in 0.016 seconds.