The generator matrix

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

generates a code of length 26 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+28x^21+73x^22+118x^23+182x^24+370x^25+554x^26+376x^27+124x^28+104x^29+66x^30+14x^31+13x^32+10x^33+10x^34+4x^35+1x^38

The gray image is a code over GF(2) with n=208, k=11 and d=84.
This code was found by Heurico 1.16 in 0.047 seconds.