The generator matrix

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

generates a code of length 30 over Z2[X]/(X^4) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+36x^24+24x^25+40x^26+72x^27+103x^28+672x^29+165x^30+672x^31+94x^32+72x^33+38x^34+24x^35+21x^36+7x^38+1x^40+5x^42+1x^50

The gray image is a linear code over GF(2) with n=240, k=11 and d=96.
This code was found by Heurico 1.16 in 0.063 seconds.