The generator matrix

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

generates a code of length 23 over Z2[X]/(X^4) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+82x^18+582x^19+1721x^20+3640x^21+6891x^22+7016x^23+6771x^24+3730x^25+1694x^26+494x^27+107x^28+20x^29+11x^30+4x^31+2x^33+2x^34

The gray image is a linear code over GF(2) with n=184, k=15 and d=72.
This code was found by Heurico 1.16 in 3.5 seconds.