The generator matrix

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

generates a code of length 37 over Z2[X]/(X^3) who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+52x^30+34x^31+87x^32+94x^33+191x^34+242x^35+160x^36+302x^37+264x^38+214x^39+124x^40+106x^41+107x^42+22x^43+10x^45+20x^46+12x^48+5x^50+1x^58

The gray image is a linear code over GF(2) with n=148, k=11 and d=60.
This code was found by Heurico 1.16 in 0.241 seconds.