The generator matrix

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

generates a code of length 26 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 25.

Homogenous weight enumerator: w(x)=1x^0+38x^25+69x^26+4x^27+7x^28+2x^29+3x^30+4x^33

The gray image is a code over GF(2) with n=208, k=7 and d=100.
This code was found by Heurico 1.16 in 0.016 seconds.