The generator matrix

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

generates a code of length 29 over Z4[X]/(X^2+2) 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 -3.24e-008 seconds.