The generator matrix

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

generates a code of length 26 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+121x^22+401x^24+256x^25+532x^26+256x^27+344x^28+110x^30+21x^32+4x^34+1x^38+1x^40

The gray image is a code over GF(2) with n=208, k=11 and d=88.
This code was found by Heurico 1.16 in 130 seconds.