The generator matrix

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

generates a code of length 28 over Z2[X]/(X^4) who´s minimum homogenous weight is 23.

Homogenous weight enumerator: w(x)=1x^0+310x^23+1758x^24+3980x^25+7479x^26+12064x^27+13986x^28+12592x^29+7926x^30+3418x^31+1393x^32+512x^33+91x^34+16x^35+6x^36+4x^37

The gray image is a linear code over GF(2) with n=224, k=16 and d=92.
This code was found by Heurico 1.16 in 16.7 seconds.