The generator matrix

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

generates a code of length 29 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+14x^27+12x^28+208x^29+12x^30+3x^32+4x^34+2x^43

The gray image is a code over GF(2) with n=232, k=8 and d=108.
This code was found by Heurico 1.16 in 2.28 seconds.