The generator matrix

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

generates a code of length 79 over Z2[X]/(X^2) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+60x^62+78x^63+309x^64+458x^65+698x^66+834x^67+1110x^68+1246x^69+1653x^70+1884x^71+2260x^72+2496x^73+2870x^74+3260x^75+3499x^76+3820x^77+3771x^78+4292x^79+3920x^80+3980x^81+3650x^82+3582x^83+3043x^84+2570x^85+2382x^86+1874x^87+1548x^88+1180x^89+946x^90+668x^91+553x^92+324x^93+300x^94+142x^95+122x^96+46x^97+44x^98+24x^99+19x^100+8x^101+9x^102+2x^103+1x^110

The gray image is a linear code over GF(2) with n=158, k=16 and d=62.
This code was found by Heurico 1.11 in 270 seconds.