The generator matrix

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

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+202x^31+350x^32+580x^33+635x^34+924x^35+869x^36+1160x^37+769x^38+1036x^39+631x^40+504x^41+239x^42+172x^43+63x^44+24x^45+19x^46+2x^47+6x^48+4x^49+2x^50

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 86.8 seconds.