The generator matrix

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

generates a code of length 87 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 83.

Homogenous weight enumerator: w(x)=1x^0+104x^83+184x^84+392x^85+319x^86+278x^87+206x^88+216x^89+122x^90+124x^91+56x^92+32x^93+5x^94+4x^95+1x^98+1x^106+2x^111+1x^128

The gray image is a code over GF(2) with n=696, k=11 and d=332.
This code was found by Heurico 1.16 in 0.796 seconds.