The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  X  X  1  1  1  1  1  1  1  1  1
 0 X^3  0  0  0  0  0  0 X^3  0 X^3 X^3  0 X^3  0  0 X^3  0  0 X^3 X^3  0 X^3
 0  0 X^3  0  0  0  0  0 X^3 X^3 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0 X^3  0  0  0
 0  0  0 X^3  0  0  0 X^3  0 X^3  0 X^3 X^3 X^3  0  0  0 X^3 X^3  0  0 X^3 X^3
 0  0  0  0 X^3  0  0 X^3  0  0 X^3 X^3 X^3  0 X^3 X^3 X^3 X^3  0 X^3  0  0 X^3
 0  0  0  0  0 X^3  0 X^3 X^3  0 X^3  0  0 X^3 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3
 0  0  0  0  0  0 X^3 X^3 X^3  0  0 X^3 X^3  0 X^3  0 X^3  0 X^3  0 X^3  0 X^3

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+20x^18+30x^20+32x^21+22x^22+832x^23+18x^24+32x^25+11x^26+10x^28+10x^30+5x^32+1x^42

The gray image is a linear code over GF(2) with n=184, k=10 and d=72.
This code was found by Heurico 1.16 in 0.25 seconds.