The generator matrix

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

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+213x^26+192x^27+430x^28+384x^29+440x^30+192x^31+173x^32+18x^34+2x^36+2x^40+1x^42

The gray image is a code over GF(2) with n=232, k=11 and d=104.
This code was found by Heurico 1.16 in 17.8 seconds.