The generator matrix

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

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+108x^20+804x^21+669x^22+1176x^23+453x^24+624x^25+162x^26+72x^27+14x^28+12x^29+1x^30

The gray image is a linear code over GF(2) with n=184, k=12 and d=80.
This code was found by Heurico 1.16 in 0.047 seconds.