The generator matrix

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

generates a code of length 46 over Z2[X]/(X^3) who´s minimum homogenous weight is 37.

Homogenous weight enumerator: w(x)=1x^0+126x^37+567x^38+1142x^39+1786x^40+2688x^41+3883x^42+5094x^43+6383x^44+7182x^45+7447x^46+7406x^47+6478x^48+5466x^49+4111x^50+2534x^51+1507x^52+876x^53+478x^54+196x^55+99x^56+46x^57+26x^58+12x^59+2x^60

The gray image is a linear code over GF(2) with n=184, k=16 and d=74.
This code was found by Heurico 1.13 in 33.3 seconds.