The generator matrix

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

generates a code of length 88 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+104x^84+190x^85+436x^86+276x^87+265x^88+166x^89+254x^90+168x^91+78x^92+26x^93+74x^94+4x^95+2x^97+2x^110+1x^118+1x^126

The gray image is a code over GF(2) with n=704, k=11 and d=336.
This code was found by Heurico 1.16 in 0.829 seconds.