The generator matrix

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

generates a code of length 37 over Z2[X]/(X^3) who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+170x^31+331x^32+672x^33+698x^34+836x^35+888x^36+990x^37+972x^38+948x^39+616x^40+526x^41+258x^42+156x^43+64x^44+50x^45+8x^46+2x^47+4x^48+2x^49

The gray image is a linear code over GF(2) with n=148, k=13 and d=62.
This code was found by Heurico 1.11 in 0.5 seconds.