The generator matrix

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

generates a code of length 37 over Z2[X]/(X^3) who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+204x^29+742x^30+1466x^31+2360x^32+3760x^33+5144x^34+6576x^35+8116x^36+8452x^37+8204x^38+7032x^39+5218x^40+3856x^41+2248x^42+1160x^43+596x^44+232x^45+110x^46+22x^47+29x^48+8x^49

The gray image is a linear code over GF(2) with n=148, k=16 and d=58.
This code was found by Heurico 1.13 in 24.6 seconds.