The generator matrix

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

generates a code of length 38 over Z2[X]/(X^4) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+74x^32+570x^33+1282x^34+2456x^35+3515x^36+5722x^37+5605x^38+5680x^39+3689x^40+2432x^41+985x^42+448x^43+177x^44+90x^45+31x^46+8x^47+2x^49+1x^50

The gray image is a linear code over GF(2) with n=304, k=15 and d=128.
This code was found by Heurico 1.16 in 6.34 seconds.