The generator matrix

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

generates a code of length 77 over Z2[X]/(X^2) who´s minimum homogenous weight is 61.

Homogenous weight enumerator: w(x)=1x^0+114x^61+222x^62+358x^63+589x^64+806x^65+1071x^66+1390x^67+1603x^68+1892x^69+2210x^70+2492x^71+2892x^72+3286x^73+3597x^74+3900x^75+4058x^76+3970x^77+4086x^78+3972x^79+3753x^80+3642x^81+3291x^82+2720x^83+2292x^84+1880x^85+1439x^86+1156x^87+808x^88+650x^89+487x^90+332x^91+218x^92+128x^93+94x^94+54x^95+36x^96+16x^97+10x^98+10x^99+5x^100+5x^102+1x^112

The gray image is a linear code over GF(2) with n=154, k=16 and d=61.
This code was found by Heurico 1.11 in 255 seconds.