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

generates a code of length 87 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 83.

Homogenous weight enumerator: w(x)=1x^0+184x^83+89x^84+242x^85+303x^86+474x^87+304x^88+208x^89+46x^90+140x^91+17x^92+18x^93+3x^94+2x^95+4x^96+12x^97+1x^160

The gray image is a code over GF(2) with n=696, k=11 and d=332.
This code was found by Heurico 1.16 in 58 seconds.