The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  X  X  X  1  1  1  X  X  X  2  2  2  X  X  1  1  2  1
 0 2X  0 2X  0  0 2X 2X  0  0 2X  0 2X 2X 2X  0  0 2X 2X  0 2X 2X  0  0  0 2X 2X  0  0
 0  0 2X 2X  0 2X 2X  0  0 2X 2X 2X 2X  0  0  0 2X 2X  0  0 2X  0 2X 2X  0 2X  0  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+50x^29+3x^30+6x^33+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 -1.01e-007 seconds.