The generator matrix

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

generates a code of length 38 over Z2[X]/(X^4) who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+212x^31+1281x^32+3770x^33+9070x^34+17976x^35+30352x^36+42980x^37+49775x^38+43910x^39+31330x^40+18042x^41+8483x^42+3268x^43+1158x^44+384x^45+93x^46+10x^47+36x^48+8x^49+3x^50+2x^52

The gray image is a linear code over GF(2) with n=304, k=18 and d=124.
This code was found by Heurico 1.16 in 266 seconds.