The generator matrix

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

generates a code of length 26 over Z4[X]/(X^3+2,2X) 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 131 seconds.