The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  X  1  1  X  1  2  X  1  0  0  0  X  1  1  1  1  1  1  X  2  1  1  1  1  2  1  1  2  1  1  X  0  X  1  0  2  1  1  1  X  1  X  X  X  1  1  1  1  1  2  1  1  X  0  0  X  1  X  1
 0  X  0  X  0  0  X X+2  0  2  X X+2  0  2  X  X X+2  0  X  0  2 X+2  0 X+2  X  0  0  X  X  2  X X+2  X  2 X+2  2  0  X X+2  X  2  X  2  X  2  0  2  0  X X+2  0 X+2 X+2  2  2  0  X  0 X+2  2 X+2 X+2  X  X  X  0  2  0  0  0  2  0  X  X  2  0  0  0  2 X+2  X  X  2  2  2 X+2  X  X  0  0 X+2  0  X  2  X  0  0
 0  0  X  X  0 X+2  X  0  0  X  X  2  2  X X+2  2  0  0  X  0  X X+2 X+2  2 X+2  X  2  2 X+2  X  2  X  X  0  0  X  0  0  2  0  0 X+2 X+2  X  X  2  X  X  2  0  0  0  0  X X+2  X  X  X  X  2 X+2  X X+2 X+2 X+2  X  0  2 X+2  X  X  2  0  0  2  2  0  X  2  0  2  2  X X+2  0  0  2  X  X  0  2  X  0  X X+2  2  0
 0  0  0  2  0  0  0  0  0  0  0  0  0  0  2  0  0  0  2  0  2  2  2  0  0  2  2  2  2  2  0  0  2  2  2  0  2  2  2  0  2  2  2  2  2  0  0  0  0  2  2  0  2  0  2  2  0  0  2  0  0  0  0  0  2  0  0  0  0  0  2  2  2  2  0  2  0  2  0  2  0  0  2  0  2  0  0  2  0  2  0  2  0  2  0  2  0
 0  0  0  0  2  0  0  0  0  0  0  2  0  2  2  2  2  0  2  2  2  0  0  0  0  2  2  0  0  2  2  2  2  0  2  2  2  0  0  0  0  2  2  0  2  2  2  2  0  2  0  2  2  2  0  2  2  2  2  2  2  0  0  0  2  2  0  0  0  0  0  2  2  2  0  2  2  0  2  2  2  2  0  0  2  0  2  2  2  0  2  2  0  2  0  0  0
 0  0  0  0  0  2  0  0  0  2  0  0  0  0  0  0  2  0  0  0  2  0  2  2  0  2  0  2  0  0  2  2  2  2  0  2  2  0  0  0  2  2  2  2  2  2  0  0  2  2  0  2  0  2  0  0  2  2  2  2  0  2  0  2  0  2  0  0  2  0  2  2  2  0  2  2  0  2  2  2  0  0  0  2  0  2  2  2  2  2  0  0  0  0  0  2  0
 0  0  0  0  0  0  2  0  0  0  2  0  0  0  0  0  2  2  2  2  2  2  0  0  0  0  2  2  0  2  2  2  2  2  0  2  2  0  2  2  2  2  0  2  0  0  2  0  2  0  2  0  2  0  2  0  2  2  2  2  2  0  2  2  2  2  2  2  0  0  0  2  0  0  0  2  0  0  2  2  0  2  2  0  2  2  0  0  2  0  2  0  2  0  2  2  0
 0  0  0  0  0  0  0  2  0  2  2  0  2  0  0  2  2  2  2  0  0  0  0  2  0  0  0  2  0  2  0  0  2  2  2  2  2  2  0  2  0  0  2  0  0  0  0  2  2  0  2  2  2  0  0  0  0  2  2  2  2  2  0  0  2  0  0  0  0  2  0  0  2  0  2  2  0  2  2  2  0  0  0  2  2  0  2  0  0  0  2  0  2  2  2  2  0
 0  0  0  0  0  0  0  0  2  0  0  0  2  0  0  0  2  2  0  2  2  0  2  2  2  2  2  0  2  2  2  0  0  0  0  0  2  2  0  2  2  0  0  2  0  2  2  0  2  2  2  2  2  2  0  2  0  2  2  0  2  2  0  0  2  2  2  0  0  0  2  0  0  2  0  0  2  0  2  2  0  0  0  2  2  0  0  0  0  2  0  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 84.

Homogenous weight enumerator: w(x)=1x^0+49x^84+30x^85+119x^86+90x^87+160x^88+226x^89+177x^90+494x^91+195x^92+766x^93+208x^94+946x^95+193x^96+1102x^97+179x^98+992x^99+148x^100+706x^101+148x^102+414x^103+125x^104+198x^105+107x^106+94x^107+94x^108+34x^109+60x^110+38x^111+40x^112+10x^113+19x^114+4x^115+15x^116+1x^118+1x^120+5x^122+3x^124+1x^138

The gray image is a code over GF(2) with n=388, k=13 and d=168.
This code was found by Heurico 1.16 in 10.3 seconds.