The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X X^2 X^2  X  1
 0 X^3+X^2  0 X^2  0  0 X^2 X^3+X^2 X^3 X^3+X^2 X^3 X^2 X^3 X^3 X^3+X^2 X^2 X^3 X^2 X^3+X^2 X^3 X^2 X^3 X^3
 0  0 X^3+X^2 X^2 X^3 X^2 X^3+X^2 X^3 X^3 X^3+X^2 X^2 X^3  0 X^3+X^2 X^2  0 X^2 X^2  0 X^2 X^2  0 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+26x^21+72x^22+78x^23+39x^24+22x^25+15x^26+2x^27+1x^34

The gray image is a linear code over GF(2) with n=184, k=8 and d=84.
This code was found by Heurico 1.16 in 0 seconds.