The generator matrix

 1  0  0  0  1  1  1 X^2  1  1 X^3+X  X  1 X^3+X  1 X^3+X^2+X  1 X^3+X  1 X^3+X X^3  0  1 X^2+X X^3+X^2+X  1
 0  1  0  0 X^2 X^3+1  1  1 X^2+1 X^3+1 X^3+X^2  1 X^3+X^2  1 X^3+X^2+X  1 X^3+X  1 X^2+X  0  1 X^3+X^2+X X^2  1  1 X^3+X^2
 0  0  1  0 X^2+1  1 X^2 X^2+1 X+1 X^2+X  1 X^2 X^2+X+1 X+1  0 X^3+X X^3+X^2+1 X^2+1 X^3+X  1 X^3+X+1  1  1 X^3 X^3+1 X^2
 0  0  0  1  1 X^2 X^2+1 X^3+1 X+1 X^2+X X^3+1 X^2+X+1 X^3  0 X^3+1 X^3+X^2 X^3+X+1 X^3+X X^3+1 X^2+X+1 X^2 X^3+X^2+X X^2+X  1 X^3+X^2+X+1 X^2

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+230x^21+1444x^22+3722x^23+7775x^24+12272x^25+14307x^26+12842x^27+7904x^28+3406x^29+1250x^30+278x^31+78x^32+12x^33+7x^34+6x^35+2x^36

The gray image is a linear code over GF(2) with n=208, k=16 and d=84.
This code was found by Heurico 1.16 in 15.1 seconds.