The generator matrix

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

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+636x^20+864x^21+1760x^22+1744x^23+1746x^24+832x^25+520x^26+16x^27+64x^28+8x^30+1x^32

The gray image is a linear code over GF(2) with n=184, k=13 and d=80.
This code was found by Heurico 1.16 in 573 seconds.