The generator matrix

 1  0  1  1  1 3X+2  1  1 2X  1  1 X+2  2 3X  1  1  1  1  X  1  1 2X+2  1  1 3X 2X  1  1 3X+2  1  1 3X  1  1  2  1  1  2  1  0 3X+2  1  1  1 3X+2  1  1  0  1  1  0  X  X  0 2X 3X  2  2  X 3X 2X+2 2X+2 3X+2  0 X+2 X+2  X  1  2  1  1  1  X  2  1  X  0  1  1  1  X  1  1  1  X  1  1
 0  1 X+1 3X+2  3  1 2X+3  0  1 3X+2 X+1  1  1  1 2X  3 3X 3X+1  1 X+1  0  1 3X  3  1  1  2 3X+3  1  1  X  1 X+3 X+2  1 2X+2  1  1  2  1  1 2X+1 3X X+3  1 3X+2  1  1  2 X+3  1  1  1  1  1  1  1  1  2  1  1  1  1  1  1  1 2X  0  1 X+2  1 3X+2  0  1  0  X  1 2X+1 X+3  3  X 2X+3  3 2X+1 3X 3X  0
 0  0  2  0  0  0  0 2X+2  2  2 2X+2  2  2 2X+2 2X  2 2X 2X 2X 2X 2X+2 2X  2 2X+2 2X+2  0 2X+2  2 2X+2  2 2X 2X 2X  0  2 2X+2  0 2X 2X 2X+2 2X+2 2X+2  2 2X+2  0  2  0  2  0 2X  2  0 2X+2 2X 2X  0 2X+2  0  2  2  2 2X  2  2  0 2X  0  2 2X+2 2X+2 2X  0 2X+2  0  0 2X+2 2X 2X+2  0  2 2X+2 2X+2  2  2  2  0  0
 0  0  0 2X+2 2X 2X+2  2  2 2X 2X 2X+2 2X+2  0  2  2  2 2X 2X+2 2X+2  0  0 2X 2X+2 2X 2X+2  2 2X  2 2X 2X 2X+2 2X  2  0 2X+2  2 2X  2 2X  2  0 2X+2  0  0  0 2X+2 2X+2  2  2  0  0  0  0  2 2X 2X+2 2X 2X  0 2X+2  2 2X+2  0 2X+2 2X  2  2  0  0 2X  2  2 2X+2  0 2X 2X  0  2  2  0 2X+2 2X+2 2X+2  2  2  0 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+171x^82+430x^83+369x^84+562x^85+403x^86+362x^87+358x^88+566x^89+297x^90+314x^91+155x^92+54x^93+20x^94+14x^95+9x^96+2x^97+1x^100+2x^106+2x^110+2x^112+1x^116+1x^118

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 0.844 seconds.