The generator matrix

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

generates a code of length 36 over Z2[X]/(X^2) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+84x^24+244x^25+499x^26+740x^27+1198x^28+1578x^29+2243x^30+2856x^31+3777x^32+4828x^33+5481x^34+6046x^35+6178x^36+6222x^37+5450x^38+4744x^39+3909x^40+3100x^41+2241x^42+1544x^43+1126x^44+614x^45+443x^46+192x^47+108x^48+52x^49+27x^50+6x^51+2x^52+2x^53+1x^56

The gray image is a linear code over GF(2) with n=72, k=16 and d=24.
This code was found by Heurico 1.11 in 91.1 seconds.