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

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+424x^82+24x^83+609x^84+264x^85+558x^86+464x^87+638x^88+240x^89+418x^90+24x^91+286x^92+8x^93+50x^94+56x^96+22x^98+9x^100+1x^144

The gray image is a code over GF(2) with n=696, k=12 and d=328.
This code was found by Heurico 1.16 in 20.3 seconds.