The generator matrix

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

generates a code of length 30 over Z2[X]/(X^3) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+177x^24+164x^25+576x^26+480x^27+1152x^28+868x^29+1332x^30+928x^31+1175x^32+492x^33+504x^34+128x^35+166x^36+12x^37+20x^38+15x^40+2x^44

The gray image is a linear code over GF(2) with n=120, k=13 and d=48.
This code was found by Heurico 1.16 in 1.02 seconds.