The generator matrix

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

generates a code of length 39 over Z2[X]/(X^4) who´s minimum homogenous weight is 33.

Homogenous weight enumerator: w(x)=1x^0+190x^33+1328x^34+2396x^35+5266x^36+7190x^37+10896x^38+10822x^39+11301x^40+7324x^41+5100x^42+2042x^43+1196x^44+350x^45+108x^46+18x^47+4x^48+2x^49+2x^51

The gray image is a linear code over GF(2) with n=312, k=16 and d=132.
This code was found by Heurico 1.16 in 23.4 seconds.