The generator matrix

 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  1  2  0  2  4  2  2  2  4  2  0  1  1  1  0  1  2  1  1  1  0  2  2  0  2  1  1  1  0  1  1  0  1  2  4  1  1  2  4  2  4  0  0  1  0  1  0  1  2  2  1
 0  2  0  2  0  0  2  6  0  0  2  6  4  0  6  4  6  4  2  6  2  4  4  6  4  0  6  2  6  4  6  6  0  6  6  4  6  2  2  2  4  2  4  2  6  0  4  6  0  2  4  2  0  0  6  4  6  6  4  4  0  6  0  2  6  6  2  2  2  2  0  2  2  2  2  0  4  4  0  0  2  4  6  0  0  0
 0  0  2  2  0  6  2  0  0  6  2  0  2  4  2  4  0  6  2  0  6  2  4  2  6  0  0  4  0  6  6  2  6  4  6  4  4  0  6  2  2  2  2  2  0  2  6  6  4  0  2  6  6  0  0  2  0  4  2  2  4  2  6  4  0  2  6  0  6  6  0  6  2  0  0  2  2  2  4  2  6  2  6  6  0  0
 0  0  0  4  0  0  0  0  0  0  0  0  0  0  4  0  0  0  0  4  0  4  4  4  4  4  0  0  0  4  0  4  4  4  0  4  0  4  0  0  4  4  4  4  0  4  4  4  4  4  4  4  4  4  0  4  0  0  0  0  4  4  0  0  4  0  4  4  0  4  0  4  0  0  4  0  0  0  4  0  0  0  0  4  0  0
 0  0  0  0  4  0  0  0  0  0  0  0  0  4  0  0  0  0  0  0  0  0  0  0  0  4  4  4  4  4  4  4  4  4  4  0  4  4  0  4  0  0  4  4  4  0  4  0  4  0  0  4  0  4  4  0  4  0  0  4  0  0  4  4  0  4  0  0  4  4  4  4  4  4  0  0  0  0  0  0  0  4  0  4  4  0
 0  0  0  0  0  4  0  0  0  0  0  0  4  0  0  0  0  4  4  0  4  0  4  4  4  4  4  4  4  4  4  4  0  4  0  0  0  4  0  0  0  0  0  4  4  4  0  0  0  4  0  0  4  0  4  0  0  4  4  0  4  4  4  4  0  4  4  4  4  0  0  0  4  4  0  4  0  4  0  0  4  0  0  0  0  0
 0  0  0  0  0  0  4  0  0  0  4  0  0  0  0  0  0  0  4  4  4  4  4  0  4  4  0  0  0  4  4  0  4  4  4  4  4  0  4  4  4  0  4  4  4  0  0  4  0  4  0  0  0  0  4  0  0  0  0  0  0  4  4  0  0  0  4  0  0  0  4  4  0  4  4  4  4  0  0  0  4  0  4  0  0  0
 0  0  0  0  0  0  0  4  0  0  4  4  4  4  0  0  0  0  0  0  4  0  4  4  0  0  4  0  4  0  4  0  4  4  0  4  0  0  4  4  0  4  0  0  4  4  4  4  4  4  0  4  4  0  0  4  0  0  4  4  0  4  0  0  4  4  4  0  0  0  0  4  0  4  4  4  4  4  0  4  0  0  4  0  0  4
 0  0  0  0  0  0  0  0  4  0  0  0  0  0  0  0  4  4  4  4  4  4  0  4  0  0  4  4  0  4  4  4  4  0  4  0  0  0  4  0  0  0  0  4  0  0  0  4  4  4  4  4  0  0  4  4  4  0  0  4  0  0  4  0  4  0  4  0  0  4  0  4  0  0  0  4  4  4  4  4  0  0  4  4  4  4
 0  0  0  0  0  0  0  0  0  4  0  4  0  0  4  4  4  0  0  0  4  4  4  0  4  0  4  0  0  0  0  0  4  4  0  4  0  4  4  4  0  0  4  4  0  0  0  0  4  4  4  0  4  0  4  4  0  4  4  0  0  0  0  4  4  0  4  0  4  4  4  0  0  4  4  4  0  4  4  4  4  4  4  4  0  0

generates a code of length 86 over Z8 who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+51x^72+64x^73+139x^74+138x^75+292x^76+300x^77+430x^78+416x^79+643x^80+730x^81+828x^82+1122x^83+1063x^84+1300x^85+1290x^86+1322x^87+1170x^88+1124x^89+860x^90+798x^91+581x^92+452x^93+373x^94+228x^95+219x^96+114x^97+109x^98+70x^99+57x^100+12x^101+44x^102+2x^103+11x^104+15x^106+7x^108+7x^110+1x^112+1x^114

The gray image is a code over GF(2) with n=344, k=14 and d=144.
This code was found by Heurico 1.16 in 25.3 seconds.