The generator matrix

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

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+236x^20+1538x^21+5253x^22+13586x^23+30655x^24+50050x^25+58878x^26+50512x^27+31624x^28+13262x^29+4585x^30+1546x^31+326x^32+62x^33+20x^34+4x^35+6x^36

The gray image is a linear code over GF(2) with n=208, k=18 and d=80.
This code was found by Heurico 1.16 in 161 seconds.