The generator matrix

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

generates a code of length 26 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+234x^24+128x^25+320x^26+128x^27+200x^28+12x^32+1x^48

The gray image is a code over GF(2) with n=208, k=10 and d=96.
This code was found by Heurico 1.16 in 0.141 seconds.