The generator matrix

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

generates a code of length 23 over Z2[X]/(X^4) who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+62x^21+114x^22+174x^23+103x^24+42x^25+5x^26+10x^27+1x^42

The gray image is a linear code over GF(2) with n=184, k=9 and d=84.
This code was found by Heurico 1.16 in 0.015 seconds.