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.