The generator matrix

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

generates a code of length 24 over Z2[X]/(X^3) who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+44x^14+12x^15+198x^16+60x^17+384x^18+352x^19+720x^20+512x^21+2636x^22+1112x^23+4276x^24+1112x^25+2656x^26+512x^27+800x^28+352x^29+388x^30+60x^31+129x^32+12x^33+32x^34+16x^36+4x^38+4x^40

The gray image is a linear code over GF(2) with n=96, k=14 and d=28.
This code was found by Heurico 1.16 in 2.63 seconds.