The generator matrix

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

generates a code of length 78 over Z2[X]/(X^2) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+136x^62+216x^63+385x^64+638x^65+853x^66+1046x^67+1328x^68+1646x^69+1942x^70+2090x^71+2509x^72+2920x^73+3382x^74+3480x^75+3695x^76+4034x^77+4005x^78+4296x^79+4020x^80+3844x^81+3419x^82+3172x^83+2728x^84+2204x^85+1881x^86+1582x^87+1178x^88+866x^89+684x^90+408x^91+359x^92+178x^93+177x^94+84x^95+42x^96+50x^97+30x^98+6x^99+10x^100+2x^101+2x^102+4x^103+1x^104+2x^105+1x^118

The gray image is a linear code over GF(2) with n=156, k=16 and d=62.
This code was found by Heurico 1.11 in 270 seconds.