The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  0  1  1  2  1  1  2 X^2+2  1  1  X  1  1  1
 0  X  0 X^2+X+2  2 X^2+X  0  X X^2 X^2+X+2 X^2+2 X+2  X X^2+2 X^2+2  X X^2+X+2  X  X  X X^2+X  2 X^2+X X^2+X  2  2
 0  0 X^2+2  0  2 X^2+2 X^2+2 X^2 X^2 X^2  2 X^2  2  0 X^2 X^2+2  0  2  0 X^2+2  0 X^2 X^2+2 X^2+2  0  2
 0  0  0 X^2+2 X^2+2 X^2 X^2+2  2  0  0 X^2+2 X^2+2  2  2 X^2  2  2 X^2 X^2+2 X^2  0  2 X^2+2 X^2+2 X^2+2  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+38x^22+160x^23+160x^24+488x^25+383x^26+486x^27+146x^28+132x^29+26x^30+8x^31+11x^32+4x^33+2x^35+2x^36+1x^42

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 0.047 seconds.