The generator matrix

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

generates a code of length 29 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+89x^26+450x^28+410x^30+28x^32+45x^34+1x^56

The gray image is a code over GF(2) with n=232, k=10 and d=104.
This code was found by Heurico 1.16 in 0.016 seconds.