The generator matrix

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

generates a code of length 72 over Z2[X]/(X^2) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+67x^60+116x^61+170x^62+284x^63+299x^64+334x^65+387x^66+368x^67+469x^68+508x^69+479x^70+482x^71+469x^72+452x^73+458x^74+480x^75+404x^76+382x^77+336x^78+286x^79+235x^80+208x^81+178x^82+134x^83+86x^84+42x^85+34x^86+12x^87+16x^88+6x^89+5x^90+2x^91+2x^92+1x^94

The gray image is a linear code over GF(2) with n=144, k=13 and d=60.
This code was found by Heurico 1.10 in 3.45 seconds.