The generator matrix

 1  0  0  0  0  0  0  0  1  1  1  0  1  1  0  1  1  1  1  1  1  1  X  X  0  1  1  1  0  X
 0  1  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  1 X+1  1  1  1  1  X  1 X+1 X+1  X  0  1
 0  0  1  0  0  0  0  0  0  0  0  0  1 X+1  1 X+1 X+1  X  1  X  1  0 X+1  X  0  X X+1  0  1  1
 0  0  0  1  0  0  0  0  0  1  1  X  0 X+1 X+1  0  1  1  X  X  1  X  0  1  0  1 X+1  0  1  0
 0  0  0  0  1  0  0  0  1  0  X  1 X+1  X  0 X+1  X  1 X+1  0 X+1 X+1  0  0  X X+1  X  1 X+1 X+1
 0  0  0  0  0  1  0  0  1  X X+1  X X+1  X X+1  0  1  0  0  X X+1 X+1 X+1  X  X  0  0 X+1  0  1
 0  0  0  0  0  0  1  0  1 X+1  0  1  X  0 X+1 X+1  X  0  X  X X+1  0  1  0  X  1  1  1 X+1  X
 0  0  0  0  0  0  0  1  X  1  X  1 X+1  0 X+1  X  1  1  X X+1  X  0  1  1 X+1 X+1  0  X  1  0

generates a code of length 30 over Z2[X]/(X^2) who´s minimum homogenous weight is 19.

Homogenous weight enumerator: w(x)=1x^0+100x^19+294x^20+562x^21+892x^22+1420x^23+2045x^24+2790x^25+3857x^26+4754x^27+5881x^28+6730x^29+6734x^30+6668x^31+5941x^32+4888x^33+3974x^34+2924x^35+2104x^36+1314x^37+732x^38+488x^39+237x^40+98x^41+65x^42+30x^43+9x^44+2x^45+2x^46

The gray image is a linear code over GF(2) with n=60, k=16 and d=19.
This code was found by Heurico 1.11 in 69.4 seconds.