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

generates a code of length 29 over Z4[X]/(X^3+2,2X) 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.