The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+16x^29+9x^30+4x^31+1x^34+1x^36

The gray image is a code over GF(2) with n=232, k=5 and d=116.
This code was found by Heurico 1.16 in 3.62e-008 seconds.