The generator matrix

 1  0  0  0  1  1  1 X^2  1  1  X X^3+X  1 X^3+X^2  1  0  1  1  1  1 X^3+X^2+X  1  1  1  1  1  1
 0  1  0  0  0 X^3+1 X^3+1  1 X^3+X^2+X X^3+X^2+X+1 X^3  1 X^2+X  1 X^3+X^2+1  1 X^3+X^2+1 X^3+X+1 X^3+X+1 X^3+X X^2 X^3+X^2 X^2+X X^3+X^2+X+1 X^2+1 X^3+X+1 X^3+X^2
 0  0  1  0  1  1 X^2 X^2+1  0 X+1  1 X^3 X+1 X^2+X+1 X^3+X X^2+1  1 X^2+X  0 X^2+X  1 X^2+X X^3+X^2+X+1 X^2+1 X^3+X^2+1 X^3 X^2+X+1
 0  0  0  1  1 X^2 X^2+1 X^2+X+1 X+1 X^2+X+1 X+1 X^3+X^2+X+1 X^2+X X^2  X  X  1 X^2+1 X^3+X X^3+X X+1 X^3+X^2+X+1 X^3  X X^2 X^3+X^2+X+1 X^2+X+1
 0  0  0  0 X^3+X^2  0 X^3+X^2  0 X^2 X^2 X^2 X^3+X^2  0 X^3  0 X^2 X^3 X^3 X^3+X^2 X^2 X^3  0 X^3+X^2 X^2 X^2 X^2  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+326x^21+1697x^22+5626x^23+14413x^24+29888x^25+49457x^26+57982x^27+51127x^28+30736x^29+13611x^30+5110x^31+1652x^32+360x^33+131x^34+18x^35+5x^36+2x^37+2x^40

The gray image is a linear code over GF(2) with n=216, k=18 and d=84.
This code was found by Heurico 1.16 in 245 seconds.