The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2  1  1  X  1  1  0  1  1 X^2+X  1 X^2+X X^2  1  0  1  1  1  1  1  0  1  1  0 X^2+X  1 X^2  1  X
 0  1  1  0 X^2+X+1  1  X X^2+X+1  1  1 X^2+X  1  0 X^2+1  1 X^2+X+1 X^2+X  1  0  1  1 X^2  1 X^2+1 X^2+X+1  X X^2+X+1 X^2  1  1 X+1  1  1 X^2+X  X X^2+X+1 X^2+X
 0  0  X  0 X^2+X  0  0 X^2 X^2  0  0 X^2  0 X^2  0  X X^2+X  X  X X^2+X X^2+X X^2+X X^2+X X^2+X X^2 X^2+X X^2+X  X  0 X^2  X X^2+X  0  0 X^2+X X^2+X X^2
 0  0  0  X  0  0 X^2+X X^2+X X^2+X  X X^2 X^2+X X^2 X^2 X^2  X X^2+X X^2+X X^2  0 X^2  X  X  X X^2+X X^2 X^2  0  X X^2  X X^2+X  X  X  X X^2+X X^2+X
 0  0  0  0 X^2  0 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0  0 X^2  0  0 X^2 X^2 X^2 X^2
 0  0  0  0  0 X^2  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2  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+92x^31+196x^32+248x^33+361x^34+428x^35+496x^36+530x^37+474x^38+432x^39+342x^40+230x^41+116x^42+60x^43+40x^44+14x^45+6x^46+12x^47+13x^48+2x^49+3x^50

The gray image is a linear code over GF(2) with n=148, k=12 and d=62.
This code was found by Heurico 1.16 in 12.9 seconds.