The generator matrix

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

generates a code of length 96 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 85.

Homogenous weight enumerator: w(x)=1x^0+112x^85+177x^86+316x^87+440x^88+516x^89+687x^90+868x^91+1006x^92+1054x^93+1211x^94+1228x^95+1351x^96+1368x^97+1160x^98+1074x^99+868x^100+740x^101+658x^102+468x^103+342x^104+244x^105+146x^106+96x^107+71x^108+46x^109+49x^110+36x^111+10x^112+16x^113+6x^114+10x^115+4x^116+1x^118+1x^122+3x^124

The gray image is a code over GF(2) with n=384, k=14 and d=170.
This code was found by Heurico 1.16 in 39.2 seconds.