The generator matrix

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

generates a code of length 23 over Z2[X]/(X^3) who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+38x^14+8x^15+120x^16+64x^17+432x^18+224x^19+1288x^20+1472x^21+3196x^22+2608x^23+3252x^24+1472x^25+1392x^26+224x^27+416x^28+64x^29+46x^30+8x^31+35x^32+16x^34+8x^36

The gray image is a linear code over GF(2) with n=92, k=14 and d=28.
This code was found by Heurico 1.16 in 1.88 seconds.