The generator matrix

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

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+122x^23+876x^24+1804x^25+4130x^26+5964x^27+6980x^28+6226x^29+3988x^30+1522x^31+859x^32+224x^33+58x^34+8x^35+4x^36+2x^37

The gray image is a linear code over GF(2) with n=224, k=15 and d=92.
This code was found by Heurico 1.16 in 4.59 seconds.