The generator matrix

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

generates a code of length 96 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+46x^86+126x^87+206x^88+316x^89+343x^90+478x^91+538x^92+622x^93+650x^94+590x^95+687x^96+582x^97+555x^98+530x^99+508x^100+394x^101+260x^102+264x^103+189x^104+90x^105+40x^106+46x^107+27x^108+28x^109+15x^110+10x^111+16x^112+12x^113+8x^114+2x^115+3x^116+4x^117+1x^118+2x^119+2x^122+1x^128

The gray image is a code over GF(2) with n=384, k=13 and d=172.
This code was found by Heurico 1.16 in 6.9 seconds.