The generator matrix

 1  0  1  1  1 X+2  1  1  0 X+2  1  1  1  1  X  1  2  1 X+2  1  1 X+2  1  1  1 X+2  1  1 X+2  1  2  1  1  1  1  1  2  1  X  1 X+2  1  1  1  0  1  0  1  1  2  0  1  1  1 X+2  1  2  X  1 X+2  1  1  1  1  1  1  X  1 X+2  1  1  1  X  1  2  1  1  1  1 X+2  1  1 X+2  1  X  2  1  1  2  1  1  1  1  1  X  2  1
 0  1  1  0  1  1  X X+3  1  1 X+3  2  X X+1  1  X  1  1  1  3  0  1 X+3  X  2  1  3  0  1  1  1 X+1  0 X+3  0 X+2  1  1  1  3  1 X+2 X+3  X  1  0  1  2  X  1  1  X X+3 X+1  1  3  1  1  3  1 X+3 X+1 X+2  0  2  3  1  2  1 X+3  1  X  1  X  1 X+3  0 X+2 X+1  1  1 X+2  1 X+1  1  X X+1  0  1  0 X+1  0  3  3  2  1 X+1
 0  0  X  0  0  0  0  0  0  2 X+2  X X+2  2  0  X  X  X X+2  2 X+2 X+2  X  X  X  X  2  X  X  2  0  X X+2 X+2  2  0  2 X+2  0 X+2  X  2  0  2 X+2 X+2  X  0  X X+2  0  2 X+2  0  X X+2  2  2 X+2  X  X X+2  X X+2  X X+2 X+2  X  0  2 X+2  0  X  X  2  0  0  0 X+2  X  2  2  2  X  X X+2  X X+2  0  2 X+2 X+2  0  0  X  2  X
 0  0  0  X  0  0  X  2  X X+2  0 X+2  X  X  0  0  2  X X+2 X+2  2  0  X  2 X+2  0  2  0  X X+2  X  2  X  X  X X+2  0  X  X  0  0  2  2  X X+2  0 X+2 X+2 X+2  0  X  2  2 X+2  X X+2  2  2  2  0  2 X+2  X  0  X  0  0  0  0  0  0  2  0 X+2  X  X X+2 X+2  X  2  2 X+2  X  X X+2  0  0  X  2  0 X+2  X  2  0  X  X  0
 0  0  0  0  X  0  0 X+2 X+2 X+2  2  X  X X+2  X X+2  0  0  0  X X+2  0  2  2  2  X  0  2 X+2  2  0  X  0 X+2  X X+2  0 X+2  2 X+2  2  0  X X+2 X+2 X+2  0  2  2  2  2 X+2  0  X  0 X+2  X  X  2 X+2 X+2  X  2  0  X  X  0  0 X+2  0  2 X+2 X+2  0  X X+2 X+2  0  2  0 X+2 X+2  X  X  0 X+2  X  2  X  0  2  2 X+2  X X+2  2 X+2
 0  0  0  0  0  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  0  0  0  0  0  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  0  2  2  2  2  0  2  0  2  2  2  2  2  0  2  2  2  2  2  0  2  2  2  2  0  2  2  0  0  0  2  2
 0  0  0  0  0  0  2  2  2  0  2  0  2  2  2  2  2  0  2  0  0  0  2  0  2  2  0  2  2  0  2  0  0  0  0  2  2  2  0  2  0  2  0  2  2  0  2  2  2  2  0  0  0  0  0  0  0  2  2  0  0  2  0  2  2  2  2  0  2  2  2  2  0  0  2  2  0  0  0  2  2  2  0  0  0  2  0  0  0  2  2  2  0  2  0  0  0

generates a code of length 97 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+139x^86+52x^87+459x^88+236x^89+783x^90+460x^91+1013x^92+748x^93+1337x^94+1020x^95+1500x^96+1140x^97+1476x^98+996x^99+1370x^100+716x^101+941x^102+496x^103+526x^104+224x^105+326x^106+48x^107+173x^108+8x^109+84x^110+58x^112+25x^114+15x^116+7x^118+2x^120+2x^122+1x^124+2x^128

The gray image is a code over GF(2) with n=388, k=14 and d=172.
This code was found by Heurico 1.16 in 25.2 seconds.