The generator matrix

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

generates a code of length 22 over Z2[X]/(X^4) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+160x^18+932x^19+1874x^20+3298x^21+3818x^22+3516x^23+1731x^24+792x^25+204x^26+32x^27+16x^28+6x^29+2x^30+2x^32

The gray image is a linear code over GF(2) with n=176, k=14 and d=72.
This code was found by Heurico 1.16 in 0.828 seconds.