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  1  1  1  X  1  0  2  X  1  1  X  X  1  1  0  1  0  1  0  1  X  1  1  1  2  1  1  X  1  1  1  1  2  1  0  1  2  1  1  0  1  1  1  X  1  1  X  1  0  X  X  X  2  1  1  1  2  X  X  1  X  1
 0  X  0  X  0  0  X X+2  0  2  X X+2  0  2  X  X X+2  0  X  0 X+2  2  0 X+2  X  0  X X+2  0 X+2  X  2  0  2  0  2 X+2  X  X X+2  X  2  X  X  0  2  X  2  0 X+2  X  0  X  2  0  X  X X+2  X  0  X X+2  X  2  X  X  2 X+2  X  X  2  0  X X+2  0  0  2  0  X X+2  0  2  0  2  X X+2  X X+2  0  0  2 X+2  0  X X+2  X  2  0
 0  0  X  X  0 X+2  X  0  0  X  X  2  2  X X+2  2  0  0  X  0 X+2  X X+2  2 X+2  X  2  0  2  X  X  0 X+2  0  X  X  0  2 X+2  0  2  X  X  X  0  0  X  X  X X+2  2  2  2  0  X X+2  X  X  2  2 X+2  0  0  X  0  2  0  0 X+2 X+2  X  0  2  0  X  X  0  X X+2  2  2 X+2  X  X  0  0  2  0  X  0  2  X  X  0  2 X+2  X  2
 0  0  0  2  0  0  0  0  0  0  0  0  0  0  2  0  0  0  2  0  2  2  2  0  0  2  0  2  2  2  2  2  2  0  0  0  0  2  0  2  0  0  2  0  2  2  2  2  2  0  2  2  2  0  0  0  2  2  2  2  2  0  0  2  2  2  2  0  2  0  2  2  0  0  0  0  0  0  2  2  0  0  2  2  2  2  0  2  0  0  0  0  0  0  0  2  0  2
 0  0  0  0  2  0  0  0  0  0  0  2  0  2  2  2  2  0  2  2  0  2  0  0  0  2  2  0  2  2  0  0  2  2  2  0  2  2  2  0  2  2  2  2  2  2  0  0  2  2  2  2  2  2  0  2  2  0  2  0  2  2  2  2  0  2  0  0  2  2  2  0  0  0  2  2  2  2  2  0  0  0  0  0  0  0  0  2  0  2  0  2  2  0  2  0  0  2
 0  0  0  0  0  2  0  0  0  2  0  0  0  0  0  0  2  0  0  0  0  2  2  2  0  2  2  2  0  0  2  2  0  2  0  0  2  0  2  0  0  2  2  2  2  0  2  0  2  0  2  2  0  0  0  0  2  0  2  0  2  0  2  2  0  0  2  2  0  2  0  0  2  2  0  2  2  0  2  2  2  0  0  0  2  2  2  0  2  0  2  0  0  0  2  0  2  0
 0  0  0  0  0  0  2  0  0  0  2  0  0  0  0  0  2  2  2  2  2  2  0  0  0  0  2  2  0  0  2  0  2  2  0  2  0  2  2  2  0  0  2  2  2  2  0  2  2  2  0  2  0  2  2  0  0  2  2  0  2  2  2  0  2  2  2  2  0  2  0  2  0  2  2  2  2  0  2  0  0  2  2  0  2  0  0  0  0  0  0  0  2  2  2  2  2  0
 0  0  0  0  0  0  0  2  0  2  2  0  2  0  0  2  2  2  2  0  0  0  0  2  0  0  0  0  2  2  2  2  2  2  2  2  2  0  2  0  0  0  0  2  2  2  2  0  2  2  0  2  2  2  0  2  2  2  0  0  2  0  0  2  2  2  0  2  0  2  0  2  0  0  0  2  0  0  0  2  2  2  0  2  0  0  0  2  2  2  0  0  2  0  2  2  2  0
 0  0  0  0  0  0  0  0  2  0  0  0  2  0  0  0  2  2  0  2  0  2  2  2  2  2  2  0  2  2  0  0  2  0  0  2  2  0  0  2  2  0  2  0  2  0  0  2  0  2  2  0  0  0  2  0  0  0  2  0  2  2  0  0  2  0  0  0  2  2  2  0  0  2  0  0  2  2  2  0  2  0  0  0  2  2  2  2  0  0  0  2  0  0  2  2  2  0

generates a code of length 98 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+60x^86+70x^87+160x^88+132x^89+229x^90+274x^91+372x^92+416x^93+491x^94+532x^95+518x^96+664x^97+548x^98+666x^99+541x^100+524x^101+448x^102+346x^103+280x^104+224x^105+181x^106+114x^107+95x^108+68x^109+66x^110+44x^111+60x^112+20x^113+14x^114+2x^115+15x^116+6x^118+4x^120+4x^122+1x^124+1x^128+1x^142

The gray image is a code over GF(2) with n=392, k=13 and d=172.
This code was found by Heurico 1.16 in 11 seconds.