The generator matrix

 1  0  0  0  1  1  1 X^2  1  1  X X^3+X^2+X  1 X^3+X^2+X  1  1  1 X^2 X^3+X^2  1  1 X^2+X X^2+X  1  1 X^3  1 X^2  X  1 X^3+X^2  1  1  1 X^3+X^2  1  1
 0  1  0  0  0 X^3+1 X^3+1  1 X^3+X^2+X X^3+X X^2+X  1 X^2+1  1 X^3+1 X^2+X+1 X^3+X+1 X^3+X  1 X^2+X+1 X^3  0 X^2 X^2+X X^2  1 X+1  1 X^2+X X^3+1 X^3  X X^2+1 X^3+X  1 X^3+X^2+X  0
 0  0  1  0  1  1 X^2 X^2+1  0 X^3+1  1 X^2 X^3+X^2+X+1 X^3+X^2+X+1 X^3+X^2+X  X X^3+X+1  1 X^2+X+1  X  X X^3+X^2+X  1 X^3+X^2+X+1 X^2+X X^3+X^2+1 X^3+X^2+X+1 X^3  X X^3  1 X^3+X^2+X X^2+1 X^3+1 X^2+X+1 X^3+X+1 X^2+X
 0  0  0  1  1 X^2 X^2+1  1 X^2+X+1 X^3+X  1 X^2+1 X^2+X+1  X X^2+X X+1 X^2+1 X^3+X^2+X+1  0 X^2 X^3+X+1  1  0 X^2+X+1  X X^2+X+1 X^3+X X^2+X+1  1 X^3+X X^3 X^3+1 X^3+1  0 X^3+1  0  X
 0  0  0  0 X^3+X^2  0 X^3+X^2  0 X^3 X^3 X^3 X^3  0  0  0 X^3 X^3  0 X^3 X^3+X^2 X^2 X^2 X^2 X^2 X^3+X^2 X^2  0 X^2  0 X^3+X^2 X^3+X^2 X^3 X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^2

generates a code of length 37 over Z2[X]/(X^4) who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+153x^30+1204x^31+3754x^32+8784x^33+16372x^34+32106x^35+43421x^36+50706x^37+42614x^38+32748x^39+17137x^40+8424x^41+3194x^42+1106x^43+291x^44+82x^45+29x^46+4x^47+4x^48+4x^49+6x^50

The gray image is a linear code over GF(2) with n=296, k=18 and d=120.
This code was found by Heurico 1.16 in 258 seconds.