The generator matrix

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

generates a code of length 39 over Z2[X]/(X^4) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+272x^32+1352x^33+3932x^34+9326x^35+18320x^36+30552x^37+42186x^38+48934x^39+43123x^40+32104x^41+18319x^42+8492x^43+3382x^44+1184x^45+448x^46+142x^47+50x^48+8x^49+11x^50+2x^51+4x^52

The gray image is a linear code over GF(2) with n=312, k=18 and d=128.
This code was found by Heurico 1.16 in 275 seconds.