The generator matrix

 1  0  0  1  1  1  X  1  1 X+2  1  1  X X+2  X X+2  1  1  0  1  1 X+2  1  1  1  1  2  2  1  0  0  1  2  1  1  1  1  1  0  1  1  2 X+2  1  1  0  0 X+2  1  2  1  1  X  1 X+2  1 X+2  1  1  X X+2 X+2 X+2  2  1  1  1  1  1  X X+2  1  1  0 X+2  1  0  1  1  X X+2  1  1  1  1  1 X+2 X+2  2  1  1  1  1  1  1 X+2  1
 0  1  0  X  1 X+3  1 X+2  0  2  1 X+1 X+2  1  1  1  X  3  1  0 X+1  1 X+2  0 X+1  1  1  X  2  1  1  X  0 X+1 X+3  2 X+2  3  1  3 X+2  X  1  0  1  1  1  0 X+3  2 X+2 X+2 X+2  3  0  0  1  2  2 X+2  1  1 X+2  1 X+3 X+3 X+2  X X+1  0  1  0 X+3  1  1  X X+2 X+1 X+3  2  1  0  X  X  1  2 X+2  1  1  2  1  0  0 X+3 X+2  2  0
 0  0  1  1 X+3 X+2  1 X+3 X+2  1  1  0  1 X+1  X  0 X+2  2  1 X+3  3 X+2  0  3 X+3  X  1  1  X X+2 X+1 X+2  1 X+2 X+1 X+2 X+3  1 X+1  X  1  1 X+3 X+1 X+1  2  X  1  0  1  1 X+2  1  3  1 X+2  1 X+1  2  1  X  2  1 X+3  3  2  0  0  X  1  1  2 X+2  0 X+2 X+3  1 X+3  0  1  X  0  0  0  3 X+1  1  0  1  3 X+1  2 X+2  3 X+3  1  0
 0  0  0  2  0  0  0  0  2  2  0  0  0  2  2  0  2  0  2  2  2  2  2  2  0  2  0  2  2  2  0  0  2  0  2  0  0  0  0  2  0  0  0  2  0  0  2  0  2  0  2  0  2  0  2  2  0  0  2  0  0  0  2  0  0  0  2  2  0  2  2  2  2  2  0  2  2  0  2  2  0  0  0  0  2  2  0  2  2  2  0  2  2  2  2  0  0
 0  0  0  0  2  0  0  0  0  0  0  2  2  2  2  2  2  0  2  0  0  0  2  0  2  2  2  2  0  0  2  0  0  0  2  2  0  2  0  0  2  2  0  2  0  2  2  2  2  0  0  0  2  0  2  0  2  0  2  2  2  2  2  2  2  0  0  2  2  0  0  2  0  0  0  2  0  0  0  2  2  0  0  0  0  0  0  2  0  2  0  0  2  2  0  0  0
 0  0  0  0  0  2  0  0  0  0  0  2  0  0  0  0  0  2  0  0  0  0  2  2  2  0  2  2  2  2  2  2  2  0  2  0  2  2  2  0  2  0  0  2  0  0  0  2  0  2  2  2  2  0  0  2  2  2  0  2  2  2  2  0  2  2  0  2  0  0  0  2  2  0  0  0  0  2  2  2  0  2  0  0  0  0  0  0  2  0  0  2  0  2  0  2  0
 0  0  0  0  0  0  2  0  0  0  0  0  0  2  0  2  2  2  0  2  2  2  2  2  2  2  0  0  0  0  2  0  0  0  2  2  0  0  0  0  2  2  2  0  2  0  0  0  2  2  0  2  0  0  0  2  2  0  2  0  0  0  2  2  0  2  2  0  0  0  2  2  0  0  0  2  2  2  2  0  2  0  0  2  2  0  2  2  0  2  2  0  0  0  2  0  0
 0  0  0  0  0  0  0  2  2  2  2  2  2  0  0  2  0  0  0  0  0  2  2  2  2  2  0  2  0  0  0  2  0  2  0  2  0  2  2  0  2  2  2  2  0  0  2  2  0  2  0  2  0  0  2  0  2  2  2  0  2  0  0  0  0  2  2  0  2  0  0  0  0  0  2  2  0  2  0  2  0  0  2  0  2  2  2  0  0  0  2  2  0  0  0  2  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+40x^86+136x^87+224x^88+628x^89+373x^90+1160x^91+438x^92+1460x^93+517x^94+1908x^95+539x^96+1928x^97+556x^98+1704x^99+479x^100+1528x^101+353x^102+984x^103+232x^104+548x^105+133x^106+240x^107+81x^108+52x^109+55x^110+12x^111+40x^112+18x^114+9x^116+3x^118+4x^120+1x^124

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 21.6 seconds.