The generator matrix

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

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+14x^21+36x^22+46x^24+70x^25+768x^26+42x^29+24x^30+15x^32+2x^33+4x^38+2x^40

The gray image is a code over GF(2) with n=208, k=10 and d=84.
This code was found by Heurico 1.16 in 23.2 seconds.