The generator matrix

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

generates a code of length 89 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+144x^82+908x^83+1575x^84+2330x^85+2749x^86+4082x^87+3250x^88+3974x^89+3218x^90+3286x^91+2306x^92+1922x^93+1147x^94+962x^95+433x^96+234x^97+106x^98+70x^99+29x^100+12x^101+2x^102+4x^103+8x^104+8x^105+2x^106+6x^108

The gray image is a code over GF(2) with n=712, k=15 and d=328.
This code was found by Heurico 1.16 in 15.9 seconds.