The generator matrix

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

generates a code of length 88 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+760x^81+1848x^82+3404x^83+4116x^84+5658x^85+6420x^86+7420x^87+7303x^88+7334x^89+6055x^90+5502x^91+3786x^92+2798x^93+1404x^94+908x^95+430x^96+210x^97+87x^98+26x^99+24x^100+24x^101+10x^102+4x^103+4x^104

The gray image is a code over GF(2) with n=704, k=16 and d=324.
This code was found by Heurico 1.16 in 54.7 seconds.