The generator matrix

 1  0  0  1  1  1 X^2+X X^3+X^2  1 X^2 X^3+X^2  1  1  1  1 X^3+X^2  1 X^3+X^2+X X^2 X^3+X X^3+X  1  X  1 X^3+X^2  1  1 X^3+X X^2  1
 0  1  0  0  1 X^3+X+1  1  1 X^2+X X^2+X  1 X^3+1 X^3+X+1  X X+1  1 X^3+X+1 X^3+X^2+X  1  1  1  X  1 X^3+X^2+X  1 X^3 X^3+X^2 X^3+X^2  1 X^2
 0  0  1  1  1 X^2+X  1 X^3+1 X^3+1  1 X^3+X^2+X X^2+1 X^3+X  0 X^2+1 X^3+X^2+X X^3  1 X+1  1 X^3+X^2  0 X^3  X X^3+X^2 X^3+X^2+X X^2+X  1 X^2+X+1 X^2
 0  0  0  X X^3 X^3+X X^3+X X^3+X^2 X^2  X X^3+X X^3+X^2+X X^3+X^2 X^3+X  0  0 X^2+X X^3  X X^3+X^2 X^3+X^2+X X^3+X^2  0 X^3+X X^2+X X^2+X X^3 X^3+X X^2 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+192x^25+934x^26+1942x^27+4256x^28+5544x^29+6995x^30+5818x^31+4149x^32+1752x^33+856x^34+220x^35+80x^36+16x^37+7x^38+2x^39+2x^40+2x^43

The gray image is a linear code over GF(2) with n=240, k=15 and d=100.
This code was found by Heurico 1.16 in 5.2 seconds.