The generator matrix

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

generates a code of length 86 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+172x^80+746x^81+1343x^82+1614x^83+2041x^84+1890x^85+1994x^86+1634x^87+1468x^88+1122x^89+769x^90+642x^91+444x^92+204x^93+165x^94+70x^95+30x^96+4x^97+16x^98+8x^99+2x^100+1x^102+1x^104+1x^108+2x^109

The gray image is a code over GF(2) with n=688, k=14 and d=320.
This code was found by Heurico 1.16 in 4.47 seconds.