The generator matrix

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

generates a code of length 23 over Z2[X]/(X^4) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+2x^22+52x^23+2x^24+4x^25+1x^26+1x^28+1x^30

The gray image is a linear code over GF(2) with n=184, k=6 and d=88.
This code was found by Heurico 1.16 in 1.05e-007 seconds.