The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+29x^40+22x^42+32x^43+31x^44+24x^45+99x^46+122x^47+133x^48+144x^49+271x^50+292x^51+345x^52+392x^53+480x^54+602x^55+541x^56+736x^57+645x^58+646x^59+509x^60+520x^61+409x^62+348x^63+302x^64+168x^65+235x^66+116x^67+267x^68+248x^69+638x^70+822x^71+1354x^72+1908x^73+2947x^74+3896x^75+4540x^76+5500x^77+5198x^78+5248x^79+4434x^80+3732x^81+3020x^82+2046x^83+1458x^84+848x^85+546x^86+238x^87+256x^88+140x^89+215x^90+132x^91+320x^92+322x^93+447x^94+590x^95+473x^96+638x^97+638x^98+736x^99+552x^100+512x^101+478x^102+438x^103+379x^104+296x^105+229x^106+178x^107+140x^108+114x^109+87x^110+24x^111+45x^112+14x^113+26x^114+6x^115+14x^116+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 98.5 seconds.