The generator matrix

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

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+40x^29+83x^30+112x^31+96x^32+352x^33+261x^34+632x^35+32x^36+808x^37+238x^38+640x^39+99x^40+304x^41+146x^42+152x^43+16x^44+32x^45+31x^46+11x^48+9x^50+1x^56

The gray image is a linear code over GF(2) with n=148, k=12 and d=58.
This code was found by Heurico 1.16 in 7.55 seconds.