The generator matrix

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

generates a code of length 26 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 23.

Homogenous weight enumerator: w(x)=1x^0+188x^23+209x^24+492x^25+384x^26+432x^27+152x^28+112x^29+52x^31+21x^32+4x^33+1x^40

The gray image is a code over GF(2) with n=208, k=11 and d=92.
This code was found by Heurico 1.16 in 20.3 seconds.