The generator matrix

 1  0  0  1  1  1 X^3+X^2+X  0  1 X^3+X X^3  1  1  1  1  1 X^2  X  1 X^3+X^2+X  1  0  1  1 X^3+X  1
 0  1  0  1  X X^2+X+1  1  1 X^2  0  1 X^2 X^3+1 X^3+X+1 X^2+X X^3+X+1  1  1 X^2+X  1  0  1 X^3+X^2+X X^3+1  1 X^3
 0  0  1  1  1  0  1 X^3 X+1  1 X^3+X^2+1  X X^2+X  1 X^2 X+1 X^3+X X^3+X^2+X+1 X^2+X+1  0 X^3+X^2+1 X^3+X^2+X+1 X^3+1 X^3+X^2+1 X^3+X^2+X  0
 0  0  0  X X^3 X^3+X X^2+X  X  X X^3+X X^2 X^3+X^2+X  0 X^2 X^2 X^3 X^3+X  X  0 X^2 X^2+X X^2+X X^2+X X^3+X^2+X X^2+X 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+90x^21+648x^22+2106x^23+3495x^24+6502x^25+7088x^26+6622x^27+3507x^28+1910x^29+576x^30+166x^31+36x^32+10x^33+8x^34+2x^35+1x^36

The gray image is a linear code over GF(2) with n=208, k=15 and d=84.
This code was found by Heurico 1.16 in 3.89 seconds.