The generator matrix

 1  0  0  1  1  1  2  2 2X+2  1  1  2  1  1 3X  1  1  1  1 X+2 3X+2  1  1 X+2  1  X 3X  1  1 2X+2  1  1  0  1  1 3X+2  1  1 3X+2  1 2X  0  1  1  1  1  1  1 3X  1  1  1 2X  1  1  1 2X  2  1  1 3X  1  1 X+2 3X 3X+2  1  1 2X  1  1  1 2X 3X+2  1  1 2X+2 2X+2  0 3X+2  1 3X  2 2X+2  1  1  1
 0  1  0  0  3  3  1  X  1 2X 2X+3  1  2  1 3X+2 3X 3X+1  X 3X+3  1  1 X+1 3X+3  0 3X+2  1  1  X 2X+3  1 3X+2 X+1  1  2  3 2X+2 X+3 2X  1  1 3X  1 2X+3  0 X+2 2X+2 X+1 3X  1 X+3 3X+2 3X+3  0  1  1 3X+1  1  1 2X+2 3X+3 2X  0 X+3 3X+2  1  2  1 2X+3  1 X+1  X X+2  1 3X X+2 X+1  1  1  1  1 X+3  X 3X  1 3X+3 3X+3  0
 0  0  1 X+1 3X+1 2X 3X+3  1 3X  X 3X  3  3 2X+3  1  1 2X+1 2X  X 3X+1 3X+2 X+1  2  1 3X+3  2 2X+1  2 X+2 3X+1  X 2X+3 2X+1  1 3X+3  1 3X+2 2X+2  2 2X+1  1 3X 2X+2 3X 2X+1 2X+3 X+3 X+1 3X+1 2X X+2 3X+2  1 3X+2 X+1  0  2  3 3X 3X+1  1  0 2X+3  1  3  1 2X 2X+2 X+1 3X+2 X+3  3 3X+3  1  2 2X  0 3X+3 X+2 2X+1  3  1  1  3 X+2 2X+2  0
 0  0  0 2X 2X  0 2X 2X 2X 2X 2X  0  0  0 2X 2X 2X 2X  0 2X 2X  0 2X  0  0  0  0  0  0  0 2X  0 2X  0 2X 2X  0  0 2X 2X  0  0 2X  0  0 2X 2X 2X  0 2X  0 2X 2X 2X  0  0 2X 2X 2X  0 2X 2X 2X  0 2X  0 2X  0  0 2X  0 2X 2X 2X 2X 2X 2X  0  0  0  0  0  0 2X  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+232x^82+658x^83+1107x^84+1024x^85+1119x^86+900x^87+963x^88+528x^89+480x^90+328x^91+271x^92+234x^93+164x^94+74x^95+56x^96+22x^97+20x^98+8x^99+1x^102+1x^104+1x^112

The gray image is a code over GF(2) with n=696, k=13 and d=328.
This code was found by Heurico 1.16 in 1.31 seconds.