The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X X^3  1  1  1 X^2  1
 0  X  0  X X^3  0 X^2+X X^2+X X^2 X^3+X^2 X^2+X X^2 X^2 X^3+X^2+X X^3+X  X X^2+X  X X^2 X^3+X^2+X X^2+X X^3 X^2
 0  0  X  X X^2 X^2+X X^2+X  0 X^3+X^2  0 X^3  X X^3+X^2+X X^3+X^2+X  X  0 X^3 X^3+X^2 X^3+X X^3+X^2 X^3+X^2 X^2 X^3+X^2+X
 0  0  0 X^3 X^3 X^3  0 X^3  0 X^3  0  0 X^3 X^3  0 X^3 X^3  0 X^3  0  0  0  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+191x^20+160x^21+484x^22+448x^23+422x^24+160x^25+136x^26+41x^28+4x^30+1x^40

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 0.031 seconds.