The generator matrix

 1  0  0  0  1  1  1 X^2  1  X X^2+X  1  X  1  1 X^2+X  1 X^2+X  1 X^2+X  1  0 X^2  1  1  X  0  1 X^2+X  1  1  1  1  X X^2  1  1
 0  1  0  0  0  1  1  1 X^2+X X^2+X  1 X^2+1  1  0 X^2+X+1 X^2  1  1 X^2+X  1  X  0 X^2+X  X X^2+X X^2  1  X  1 X+1 X^2+X+1 X^2+X X^2  1 X^2 X^2  X
 0  0  1  0  1  1  0  1 X^2  1 X^2+X+1 X+1 X^2 X+1 X^2+X  0 X^2  1 X^2+X+1 X^2+X X^2+X  1  1 X+1 X^2+1  1 X+1  X  X  1 X^2+1 X^2+X+1  X X^2+X+1  1 X^2+X X^2+X
 0  0  0  1  1  0  1 X+1 X^2+X+1  1  X X+1 X^2+1  0  X  1 X+1  X  0  1 X^2 X^2+X X+1 X^2+X+1 X^2+1  0  1 X^2+1  1 X^2+X X^2+X+1 X^2+X  X X^2+1  1  1 X^2
 0  0  0  0 X^2  0  0  0  0  0  0 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 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0  0
 0  0  0  0  0 X^2  0  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0  0 X^2 X^2
 0  0  0  0  0  0 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2  0  0  0 X^2  0 X^2 X^2  0  0 X^2  0 X^2  0  0  0 X^2 X^2 X^2  0 X^2  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+72x^29+397x^30+568x^31+1469x^32+1680x^33+2825x^34+2958x^35+4430x^36+3800x^37+4548x^38+3086x^39+3098x^40+1456x^41+1277x^42+586x^43+338x^44+96x^45+39x^46+34x^47+8x^48+1x^50+1x^58

The gray image is a linear code over GF(2) with n=148, k=15 and d=58.
This code was found by Heurico 1.16 in 19.1 seconds.