The generator matrix

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

generates a code of length 28 over Z2[X]/(X^4) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+434x^22+1808x^23+6140x^24+14640x^25+29382x^26+50300x^27+56188x^28+50496x^29+30358x^30+14728x^31+5467x^32+1520x^33+490x^34+140x^35+44x^36+8x^38

The gray image is a linear code over GF(2) with n=224, k=18 and d=88.
This code was found by Heurico 1.16 in 190 seconds.