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

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+206x^82+8x^83+352x^84+200x^85+478x^86+576x^87+617x^88+544x^89+459x^90+184x^91+186x^92+24x^93+147x^94+71x^96+13x^98+18x^100+7x^102+2x^104+2x^106+1x^152

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 29.9 seconds.