The generator matrix

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

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+18x^21+125x^22+77x^24+12x^25+18x^26+2x^28+2x^29+1x^30

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 0.047 seconds.