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

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+37x^88+80x^89+88x^90+98x^91+111x^92+136x^93+197x^94+244x^95+230x^96+200x^97+171x^98+112x^99+75x^100+64x^101+34x^102+36x^103+34x^104+24x^105+16x^106+14x^107+16x^108+8x^109+4x^110+8x^111+6x^112+2x^116+1x^118+1x^170

The gray image is a code over GF(2) with n=384, k=11 and d=176.
This code was found by Heurico 1.16 in 0.969 seconds.