The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+57x^26+140x^27+262x^28+104x^29+261x^30+140x^31+57x^32+1x^42+1x^46

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.