The generator matrix

 1  0  0  1  1  1 X+2 X+2  1  1 X^2+X  1  1 X^2  1  1  0 X^2+2 X+2  1  0  1 X^2+2  1  2  1
 0  1  0  0 X^2+3 X+1  1  1 X^2+X X^2+1  2  X X^2+3  1 X^2+X+1 X^2+X+3  1  1  X X+2  1 X^2  1 X^2+X+1  1  1
 0  0  1 X+1 X+1  0  1 X^2+X  2  1  1  1 X^2+X X^2+X+3  3 X^2+X+2 X^2+X  3  1 X+2 X+3 X^2+2 X^2+3  0  X X^2+3
 0  0  0 X^2 X^2+2  2 X^2  2  0 X^2+2  0  2 X^2  0  0 X^2+2  2  2 X^2+2 X^2 X^2+2  2 X^2+2 X^2+2  0  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+354x^22+920x^23+2047x^24+3240x^25+3309x^26+3324x^27+1989x^28+764x^29+324x^30+60x^31+32x^32+12x^33+5x^34+3x^36

The gray image is a code over GF(2) with n=208, k=14 and d=88.
This code was found by Heurico 1.16 in 23.5 seconds.