The generator matrix

 1  0  1  1  1 X+2  1  1  0  1  1 X+2  0  1  1 X+2  1  1  X  1  1  1  1  0  1  1  0 X+2  1  1  1  1  0  1 X+2  1  0  1  1  1  2 X+2  1  1  1 X+2  1 X+2  1  1  0  1  1  1  1 X+2  1  1  0  1  1  0  1  1  X  1  X  1  1  1  1 X+2  1  1  1  1  X  1  1  1  1  1  1  1  2 X+2  X X+2 X+2  1  1 X+2  1  1  1  1  1
 0  1 X+1 X+2  1  1  0 X+1  1 X+2  3  1  1 X+2 X+1  1  3  0  1  2 X+1 X+3 X+2  1  3  0  1  1 X+2  3 X+2  3  1 X+1  1  0  1  0  3 X+2  1  1 X+1  2 X+3  1  1  1 X+2  0  1  3  0  X  X  1  0 X+1  1  1  X  1 X+1 X+2  1  3  1 X+1  1  X  3  1 X+2  0  1  X  1  2 X+1  0 X+1 X+1  2 X+3  1  1  1  1  1  X X+2  1  0 X+3  3  0  0
 0  0  2  0  0  0  0  0  0  0  0  0  0  0  2  0  0  0  0  0  2  2  2  2  2  2  0  2  2  2  2  0  2  2  2  0  2  0  0  2  2  0  0  0  2  0  2  2  0  0  0  0  2  2  0  2  0  0  2  0  2  0  2  2  0  0  0  2  2  2  2  0  0  0  2  0  2  0  2  2  2  0  0  0  2  0  0  2  0  0  2  2  2  2  0  2  0
 0  0  0  2  0  0  0  0  0  0  0  0  0  2  0  2  2  2  2  2  0  0  2  2  2  2  0  2  2  2  0  0  2  2  0  2  0  2  2  0  0  2  0  2  0  0  0  0  2  0  2  2  0  2  0  0  0  2  2  0  2  0  2  0  0  0  0  0  0  2  2  0  2  2  2  0  0  2  2  2  0  0  0  0  2  2  2  2  0  2  0  2  2  0  0  0  0
 0  0  0  0  2  0  0  0  0  0  0  2  2  0  0  2  2  0  0  0  2  2  0  0  2  0  2  2  2  0  2  0  2  2  0  2  2  0  2  0  0  0  2  2  0  0  0  2  2  0  2  2  2  0  2  0  2  0  0  0  2  2  2  0  2  2  2  2  2  2  0  0  2  0  2  2  0  0  0  0  2  2  0  2  2  0  0  0  0  2  0  0  0  0  2  0  0
 0  0  0  0  0  2  0  0  0  0  2  2  2  0  2  0  2  0  0  0  0  2  0  2  0  0  0  2  0  0  0  2  2  0  2  2  2  2  0  2  2  2  0  0  0  2  0  0  0  0  2  0  2  2  2  2  2  0  0  0  0  0  0  2  2  2  0  0  2  0  2  2  0  2  2  0  2  2  0  0  2  2  0  2  0  2  2  0  2  2  0  0  2  0  2  0  2
 0  0  0  0  0  0  2  0  0  2  2  0  0  2  2  0  2  0  0  2  0  2  2  2  0  0  2  0  2  2  0  0  2  2  0  0  0  2  0  2  2  2  2  2  2  2  0  2  2  0  0  0  2  0  2  0  0  2  2  0  0  0  2  0  0  2  2  2  0  0  2  2  2  0  0  0  0  0  2  0  2  0  2  0  0  2  0  0  0  2  2  2  0  0  0  0  2
 0  0  0  0  0  0  0  2  0  2  0  0  0  2  2  2  0  2  2  2  2  0  2  0  0  2  0  0  0  0  0  2  0  2  0  2  0  0  0  0  0  2  2  0  2  2  2  0  2  0  0  0  2  2  0  2  2  0  2  0  2  2  0  2  2  0  0  0  2  2  2  0  0  2  2  0  2  0  0  0  2  2  2  0  0  0  2  2  0  2  0  0  2  0  2  2  0
 0  0  0  0  0  0  0  0  2  0  2  2  0  0  2  0  2  2  2  2  2  0  0  2  2  0  2  0  0  2  2  0  2  0  0  2  2  0  0  0  0  2  0  0  2  2  0  0  0  2  0  2  2  0  0  2  0  2  0  2  2  0  2  2  0  2  0  2  0  0  0  2  2  2  2  2  0  2  0  0  2  2  2  0  0  0  0  2  2  0  2  2  0  2  0  0  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+54x^86+8x^87+209x^88+108x^89+389x^90+200x^91+567x^92+400x^93+704x^94+560x^95+683x^96+520x^97+669x^98+560x^99+688x^100+400x^101+548x^102+200x^103+343x^104+108x^105+165x^106+8x^107+41x^108+14x^110+6x^112+7x^114+12x^116+6x^118+6x^120+2x^122+2x^124+2x^126+2x^132

The gray image is a code over GF(2) with n=388, k=13 and d=172.
This code was found by Heurico 1.16 in 7.48 seconds.