The generator matrix

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

generates a code of length 28 over Z2[X]/(X^4) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+17x^24+168x^25+241x^26+376x^27+447x^28+392x^29+234x^30+136x^31+14x^32+16x^33+3x^34+1x^36+1x^38+1x^46

The gray image is a linear code over GF(2) with n=224, k=11 and d=96.
This code was found by Heurico 1.16 in 0.031 seconds.