The generator matrix

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

generates a code of length 30 over Z2[X]/(X^4) who´s minimum homogenous weight is 25.

Homogenous weight enumerator: w(x)=1x^0+440x^25+1853x^26+4136x^27+8073x^28+11240x^29+13893x^30+11598x^31+8083x^32+4060x^33+1583x^34+360x^35+169x^36+36x^37+7x^38+2x^39+2x^40

The gray image is a linear code over GF(2) with n=240, k=16 and d=100.
This code was found by Heurico 1.16 in 17.1 seconds.