The generator matrix

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

generates a code of length 31 over Z2[X]/(X^3) who´s minimum homogenous weight is 23.

Homogenous weight enumerator: w(x)=1x^0+168x^23+559x^24+1154x^25+2146x^26+3256x^27+5434x^28+6480x^29+9259x^30+8508x^31+9153x^32+6712x^33+5713x^34+3184x^35+2042x^36+1000x^37+437x^38+244x^39+59x^40+14x^41+13x^42

The gray image is a linear code over GF(2) with n=124, k=16 and d=46.
This code was found by Heurico 1.13 in 18.4 seconds.