The generator matrix

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

generates a code of length 23 over Z2[X]/(X^4) who´s minimum homogenous weight is 19.

Homogenous weight enumerator: w(x)=1x^0+202x^19+1036x^20+1662x^21+3423x^22+3742x^23+3559x^24+1596x^25+862x^26+198x^27+74x^28+22x^29+3x^30+2x^31+2x^32

The gray image is a linear code over GF(2) with n=184, k=14 and d=76.
This code was found by Heurico 1.16 in 0.906 seconds.