The generator matrix

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

generates a code of length 96 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+107x^88+108x^89+315x^90+188x^91+394x^92+220x^93+353x^94+252x^95+364x^96+244x^97+333x^98+244x^99+305x^100+180x^101+216x^102+84x^103+78x^104+16x^105+31x^106+16x^108+19x^110+8x^112+9x^114+5x^116+4x^118+1x^128+1x^136

The gray image is a code over GF(2) with n=384, k=12 and d=176.
This code was found by Heurico 1.16 in 2.05 seconds.