The generator matrix

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

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+244x^27+228x^28+216x^29+110x^30+120x^31+43x^32+56x^33+4x^35+2x^38

The gray image is a code over GF(2) with n=232, k=10 and d=108.
This code was found by Heurico 1.16 in 8.2 seconds.