The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  0  X X^2+2  X  0  X X^2+2  X  2  X X^2 X^2
 0  X X^2+2 X^2+X  0 X^2+X X^2+2 X+2  2 X^2+X+2 X^2 X+2  2 X^2+X+2 X^2  X X^2+X  X X+2  X X^2+X  X X+2  X X^2+X+2  X  X  X  0
 0  0  2  2  2  0  0  2  2  2  0  0  0  0  2  2  0  2  2  0  2  0  0  2  2  0  0  2  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+132x^28+112x^30+9x^32+2x^40

The gray image is a code over GF(2) with n=232, k=8 and d=112.
This code was found by Heurico 1.16 in 0.016 seconds.