The generator matrix

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

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+140x^22+1076x^23+2904x^24+7260x^25+15865x^26+22352x^27+31205x^28+23114x^29+16186x^30+7252x^31+2553x^32+832x^33+253x^34+56x^35+9x^36+10x^37+4x^38

The gray image is a linear code over GF(2) with n=224, k=17 and d=88.
This code was found by Heurico 1.16 in 45.3 seconds.