The generator matrix

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

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+89x^84+148x^85+232x^86+504x^87+234x^88+508x^89+128x^90+48x^91+47x^92+52x^93+20x^94+8x^95+12x^96+12x^97+4x^98+1x^168

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 0.859 seconds.