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

generates a code of length 33 over Z2[X]/(X^4) who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+88x^30+190x^32+512x^33+176x^34+56x^38+1x^64

The gray image is a linear code over GF(2) with n=264, k=10 and d=120.
This code was found by Heurico 1.16 in 65.7 seconds.