The generator matrix

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

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+98x^29+159x^30+188x^31+267x^32+350x^33+641x^34+796x^35+952x^36+1206x^37+1109x^38+872x^39+540x^40+306x^41+251x^42+172x^43+123x^44+88x^45+44x^46+20x^47+4x^48+4x^50+1x^60

The gray image is a linear code over GF(2) with n=148, k=13 and d=58.
This code was found by Heurico 1.16 in 5.11 seconds.