The generator matrix

 1  1  1  1  1  1  1  1  X  1  0  1  1  X  2  1  1  1  1  1  X 2X  X 2X+2  X  X  X  X  1
 0  X  2 3X+2 2X X+2 2X+2 3X 3X+2  0  X 3X+2  2 3X  X 3X 2X 2X+2 X+2  X X+2  X  X  X  0  2 2X 2X+2  0

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

Homogenous weight enumerator: w(x)=1x^0+6x^28+108x^29+6x^30+1x^32+4x^33+2x^34

The gray image is a code over GF(2) with n=232, k=7 and d=112.
This code was found by Heurico 1.16 in -3.24e-008 seconds.