The generator matrix

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

generates a code of length 87 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+248x^80+882x^81+1666x^82+2284x^83+2907x^84+3534x^85+3533x^86+3626x^87+3606x^88+3024x^89+2627x^90+1922x^91+1148x^92+718x^93+450x^94+294x^95+113x^96+66x^97+54x^98+18x^99+25x^100+16x^101+5x^102+1x^106

The gray image is a code over GF(2) with n=696, k=15 and d=320.
This code was found by Heurico 1.16 in 15.4 seconds.