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

generates a code of length 88 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+70x^82+224x^83+316x^84+410x^85+394x^86+430x^87+520x^88+424x^89+382x^90+336x^91+271x^92+166x^93+74x^94+34x^95+1x^96+8x^98+16x^99+9x^100+8x^101+1x^104+1x^144

The gray image is a code over GF(2) with n=704, k=12 and d=328.
This code was found by Heurico 1.16 in 1.16 seconds.