The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  1  1
 0 X^3  0  0  0  0  0 X^3  0 X^3  0 X^3  0 X^3 X^3  0  0 X^3  0  0 X^3 X^3 X^3
 0  0 X^3  0  0  0 X^3 X^3  0 X^3  0  0 X^3  0 X^3  0 X^3  0  0 X^3 X^3 X^3  0
 0  0  0 X^3  0  0 X^3  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3  0
 0  0  0  0 X^3  0 X^3  0 X^3 X^3  0 X^3  0  0 X^3 X^3  0  0 X^3 X^3  0  0 X^3
 0  0  0  0  0 X^3 X^3  0 X^3  0 X^3 X^3  0 X^3  0 X^3 X^3  0  0  0 X^3 X^3  0

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+25x^20+32x^22+384x^23+59x^24+10x^28+1x^44

The gray image is a linear code over GF(2) with n=184, k=9 and d=80.
This code was found by Heurico 1.16 in 3.81e-009 seconds.