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

generates a code of length 87 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+47x^82+80x^83+100x^84+32x^85+498x^86+544x^87+497x^88+32x^89+83x^90+80x^91+41x^92+12x^94+1x^172

The gray image is a code over GF(2) with n=696, k=11 and d=328.
This code was found by Heurico 1.16 in 1.11 seconds.