The generator matrix

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

generates a code of length 23 over Z2[X]/(X^4) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+291x^20+64x^21+584x^22+128x^23+707x^24+64x^25+152x^26+49x^28+8x^32

The gray image is a linear code over GF(2) with n=184, k=11 and d=80.
This code was found by Heurico 1.16 in 3.23 seconds.