The generator matrix

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

generates a code of length 37 over Z2[X]/(X^4) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+140x^32+698x^33+1373x^34+1920x^35+2649x^36+2936x^37+2747x^38+1860x^39+1183x^40+518x^41+195x^42+108x^43+27x^44+24x^45+5x^46

The gray image is a linear code over GF(2) with n=296, k=14 and d=128.
This code was found by Heurico 1.16 in 1.69 seconds.