The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2+2  1  1 X+2  1  1  1  1  0 X^2+X  1  1  1 X+2 X^2+2  1  1  1
 0  1 X+1 X^2+X X^2+1  1 X^2+2 X^2+X+3  1 X+2  3  1  0 X^2+X X+1 X^2+1  1  1 X^2+2 X^2+X  3  1  1 X^2+X+3 X+2 X^2+X
 0  0  2  0  0  0  0  2  0  2  2  2  0  0  0  2  0  2  2  2  0  0  2  2  2  0
 0  0  0  2  0  0  2  2  0  2  0  2  0  2  0  0  2  0  2  2  2  2  0  2  0  0
 0  0  0  0  2  0  2  0  2  2  2  2  0  2  2  2  2  0  2  0  2  0  2  2  2  0
 0  0  0  0  0  2  0  2  2  2  0  2  2  2  2  2  0  0  2  0  0  2  2  0  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+1026x^24+1812x^26+1014x^28+110x^30+5x^32+4x^34+2x^36+1x^38

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 11.8 seconds.