The generator matrix

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

generates a code of length 37 over Z2[X]/(X^4) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+68x^34+116x^35+159x^36+376x^37+146x^38+52x^39+71x^40+32x^41+2x^42+1x^68

The gray image is a linear code over GF(2) with n=296, k=10 and d=136.
This code was found by Heurico 1.16 in 0.031 seconds.