The generator matrix

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

generates a code of length 27 over Z2[X]/(X^4) who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+88x^21+838x^22+2872x^23+7569x^24+14280x^25+25349x^26+28548x^27+25984x^28+14792x^29+7176x^30+2464x^31+864x^32+184x^33+45x^34+4x^35+14x^36

The gray image is a linear code over GF(2) with n=216, k=17 and d=84.
This code was found by Heurico 1.16 in 45.8 seconds.