The generator matrix

 1  0  0  1  1  1  2  0  1  1  0  1  1  2  4  1  0  1  4  1  2  0  1  4  1  0  4  1  4  2  1  1  1  1  1  1  2  1  1  6  1  1  1  2  1  4  1  0  4  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  1  0  1  2  3  1  0  0  5  1  2  7  1  2  6  1  2  0  1  1  2  3  1  5  1  1  1  2  1  7  7  5  2  2  7  1  6  5  0  3  3  2  0  2  1  4  1  0  0  0  0  0  0  0  0  0  0  0  0  0  4  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
 0  0  1  1  1  0  1  1  2  3  2  3  2  3  1  0  2  3  1  2  1  1  1  1  2  2  3  0  1  3  0  3  2  1  3  3  2  2  2  1  2  0  1  1  1  2  0  0  1  0  0  0  0  0  0  0  0  0  0  0  0  4  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
 0  0  0  2  0  6  0  6  2  0  2  2  0  2  0  4  2  6  2  0  0  2  6  4  6  6  2  2  0  2  2  6  6  4  2  6  0  6  6  4  6  4  4  2  0  0  2  4  6  0  0  0  0  0  4  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  0  4  0  0  0  0  4  0  0  4  4  4  4  0  4  0  4  0  4  4  4  0  0  0  0  0  0  4  0  4  0  0  4  4  4  0  0  4  0  0  0  4  4  4  4  0  0  0  0  0  4  4  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  0  0  4  0  0  0  4  0  4  4  0  4  0  4  0  4  4  4  0  4  4  0  0  4  0  4  0  0  0  0  4  4  4  0  0  4  4  4  4  4  0  4  4  4  0  4  4  0  0  0  4  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  0  0  0  0  4  0  0  4  4  4  4  4  0  4  4  4  0  0  0  0  4  0  0  0  4  0  4  4  0  4  0  0  0  0  4  0  0  4  4  0  4  4  4  0  4  0  0  4  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  0  0
 0  0  0  0  0  0  0  4  0  4  4  4  0  4  4  0  4  0  0  0  4  0  0  4  4  0  4  4  0  4  0  4  4  4  4  4  4  4  4  4  4  0  4  0  0  0  0  0  0  4  4  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  0
 0  0  0  0  0  0  0  0  4  4  4  0  4  0  0  4  0  4  4  4  4  0  4  4  4  4  4  0  0  4  0  0  4  0  0  0  0  0  4  4  4  0  0  0  4  0  0  0  4  4  4  4  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

generates a code of length 78 over Z8 who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+16x^40+6x^41+31x^42+38x^43+72x^44+70x^45+125x^46+222x^47+255x^48+362x^49+444x^50+560x^51+684x^52+758x^53+780x^54+746x^55+657x^56+664x^57+529x^58+396x^59+302x^60+168x^61+127x^62+80x^63+56x^64+28x^65+38x^66+66x^67+74x^68+208x^69+334x^70+846x^71+1013x^72+2074x^73+2260x^74+4604x^75+3988x^76+6536x^77+5004x^78+6484x^79+4108x^80+4640x^81+2306x^82+2124x^83+964x^84+828x^85+294x^86+206x^87+99x^88+48x^89+40x^90+30x^91+66x^92+86x^93+115x^94+228x^95+303x^96+352x^97+496x^98+552x^99+672x^100+816x^101+802x^102+770x^103+664x^104+584x^105+442x^106+388x^107+268x^108+176x^109+129x^110+82x^111+63x^112+26x^113+30x^114+10x^115+6x^116+2x^117+10x^118+5x^120

The gray image is a code over GF(2) with n=312, k=16 and d=80.
This code was found by Heurico 1.16 in 99 seconds.