The generator matrix

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

generates a code of length 28 over Z2[X]/(X^3) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+161x^24+32x^25+64x^26+224x^27+64x^28+224x^29+64x^30+32x^31+154x^32+3x^40+1x^48

The gray image is a linear code over GF(2) with n=112, k=10 and d=48.
This code was found by Heurico 1.16 in 0.489 seconds.