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 X^3  0  0  0  0  0 X^3  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3  0 X^3  0 X^3  0
 0  0 X^3  0  0  0  0 X^3  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3  0  0 X^3  0 X^3  0 X^3  0 X^3
 0  0  0 X^3  0  0  0 X^3  0 X^3 X^3  0  0  0 X^3  0  0 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3
 0  0  0  0 X^3  0  0 X^3  0 X^3  0 X^3  0 X^3  0 X^3  0  0  0 X^3  0 X^3 X^3  0 X^3 X^3
 0  0  0  0  0 X^3  0 X^3 X^3  0  0 X^3  0 X^3 X^3  0  0 X^3  0  0 X^3 X^3 X^3 X^3  0  0
 0  0  0  0  0  0 X^3 X^3 X^3  0 X^3  0  0 X^3  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3  0  0 X^3

generates a code of length 26 over Z2[X]/(X^4) 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 linear code over GF(2) with n=208, k=10 and d=84.
This code was found by Heurico 1.16 in 23.5 seconds.