The generator matrix

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

generates a code of length 26 over Z2[X]/(X^4) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+106x^20+792x^21+2732x^22+6794x^23+14760x^24+25222x^25+30190x^26+25054x^27+15122x^28+6958x^29+2456x^30+694x^31+155x^32+18x^33+14x^34+2x^35+2x^37

The gray image is a linear code over GF(2) with n=208, k=17 and d=80.
This code was found by Heurico 1.16 in 43.1 seconds.