The generator matrix

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

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+82x^19+283x^20+512x^21+744x^22+890x^23+756x^24+480x^25+241x^26+62x^27+15x^28+16x^29+6x^30+6x^31+1x^32+1x^34

The gray image is a linear code over GF(2) with n=184, k=12 and d=76.
This code was found by Heurico 1.16 in 0.062 seconds.