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

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

Homogenous weight enumerator: w(x)=1x^0+34x^84+154x^85+58x^86+208x^87+28x^88+356x^89+4x^90+160x^91+18x^93+1x^104+1x^106+1x^130

The gray image is a code over GF(2) with n=704, k=10 and d=336.
This code was found by Heurico 1.16 in 0.782 seconds.