The generator matrix

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

generates a code of length 31 over Z2[X]/(X^3) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+59x^22+122x^23+224x^24+332x^25+436x^26+470x^27+1116x^28+648x^29+4300x^30+860x^31+4315x^32+800x^33+1136x^34+484x^35+432x^36+248x^37+200x^38+106x^39+52x^40+20x^41+12x^42+6x^43+4x^44+1x^54

The gray image is a linear code over GF(2) with n=124, k=14 and d=44.
This code was found by Heurico 1.16 in 6.45 seconds.