The generator matrix

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

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+176x^22+236x^23+532x^24+664x^25+936x^26+656x^27+492x^28+232x^29+104x^30+4x^31+59x^32+4x^36

The gray image is a code over GF(2) with n=208, k=12 and d=88.
This code was found by Heurico 1.16 in 0.109 seconds.