The generator matrix

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

generates a code of length 65 over Z2[X]/(X^2) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+29x^40+54x^41+79x^42+106x^43+183x^44+208x^45+254x^46+348x^47+363x^48+464x^49+536x^50+550x^51+704x^52+688x^53+758x^54+796x^55+734x^56+890x^57+854x^58+950x^59+1077x^60+1094x^61+1294x^62+1408x^63+1339x^64+1372x^65+1358x^66+1256x^67+1223x^68+1150x^69+1083x^70+944x^71+888x^72+874x^73+741x^74+744x^75+767x^76+710x^77+641x^78+638x^79+555x^80+476x^81+394x^82+318x^83+243x^84+178x^85+155x^86+120x^87+75x^88+30x^89+38x^90+12x^91+11x^92+4x^93+7x^94+2x^95

The gray image is a linear code over GF(2) with n=130, k=15 and d=40.
This code was found by Heurico 1.16 in 99.4 seconds.