The generator matrix

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

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+162x^86+48x^87+427x^88+244x^89+675x^90+452x^91+1114x^92+796x^93+1356x^94+1036x^95+1543x^96+1048x^97+1539x^98+976x^99+1181x^100+760x^101+1016x^102+512x^103+617x^104+212x^105+243x^106+44x^107+159x^108+12x^109+86x^110+4x^111+56x^112+31x^114+14x^116+12x^118+4x^120+3x^124+1x^132

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 25.7 seconds.