The generator matrix

 1  0  1  1  1 X+2  1  1  X  1  1 3X+2  1  1  2  1  1 2X  1  1  1 2X 3X+2  1  1  1  X  1  1
 0  1 X+1 3X+2 2X+3  1 X+2 3X+3  1  X X+1  1  2 2X+1  1 2X  3  1 3X 2X+2 X+3  1  1  1  0  0 X+2  0 3X
 0  0 2X+2  0 2X  2  2  2 2X+2 2X+2 2X  0  0 2X  0 2X+2  2 2X+2 2X 2X+2  0 2X+2 2X  2 2X  0 2X+2 2X+2  0
 0  0  0 2X 2X 2X  0 2X  0 2X  0 2X 2X  0 2X  0  0  0  0 2X 2X 2X  0 2X 2X 2X 2X 2X 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+190x^26+192x^27+536x^28+256x^29+500x^30+192x^31+153x^32+14x^34+12x^36+2x^40

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 0.032 seconds.