The generator matrix

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

generates a code of length 97 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+150x^84+550x^85+869x^86+1602x^87+2362x^88+3308x^89+4525x^90+5060x^91+6086x^92+7594x^93+8639x^94+9306x^95+9841x^96+10320x^97+10347x^98+9790x^99+8926x^100+7804x^101+6531x^102+5242x^103+4010x^104+2858x^105+1975x^106+1344x^107+876x^108+510x^109+305x^110+150x^111+56x^112+72x^113+25x^114+14x^115+10x^116+6x^117+4x^119+2x^120+2x^121

The gray image is a code over GF(2) with n=388, k=17 and d=168.
This code was found by Heurico 1.13 in 650 seconds.