The generator matrix

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

generates a code of length 31 over Z2[X]/(X^3) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+16x^18+4x^19+56x^20+12x^21+154x^22+60x^23+205x^24+220x^25+582x^26+488x^27+1792x^28+792x^29+3240x^30+952x^31+3386x^32+792x^33+1900x^34+468x^35+592x^36+220x^37+186x^38+76x^39+87x^40+12x^41+62x^42+24x^44+4x^46+1x^48

The gray image is a linear code over GF(2) with n=124, k=14 and d=36.
This code was found by Heurico 1.16 in 4.48 seconds.