The generator matrix

 1  0  0  0  1  1  1  1 X^2  1  0  X  1  1 X^2  X  1  1  1  1  1 X^2+X  X X^2+X  1  X  1  X  X  X  1  1  1  1  1  1  1
 0  1  0  0  0 X^2  1 X^2+1  1 X+1 X^2+X  1 X^2+1 X^2+X  1  1 X^2+X X^2+X+1 X^2+X X+1  X  1 X^2+X  1 X^2+X  1 X^2+X+1  X  1  0  1  0  X  X  1  1 X^2
 0  0  1  0  0  1 X^2+1  X X+1  1  1 X^2 X^2+X X^2+X+1  1 X+1  0 X^2+X X^2+X X+1  1  X  1  0  0 X^2+X+1 X^2  1  1  X X^2  1 X^2+X+1 X^2 X^2+1 X+1 X^2
 0  0  0  1 X+1 X+1 X^2  1  1  1 X^2+1 X^2+1 X^2+X  X  0  X X^2 X^2 X^2+1 X^2+1 X+1 X^2+X+1 X+1 X^2+X  X  1 X^2+1  0  1  1 X+1  X  X X^2+X  X X+1  X
 0  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0  0 X^2  0  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  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+156x^31+347x^32+596x^33+802x^34+846x^35+944x^36+940x^37+910x^38+854x^39+728x^40+492x^41+270x^42+186x^43+88x^44+20x^45+2x^46+6x^47+4x^48

The gray image is a linear code over GF(2) with n=148, k=13 and d=62.
This code was found by Heurico 1.16 in 1.29 seconds.