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

generates a code of length 88 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+23x^82+62x^83+40x^84+38x^85+33x^86+28x^87+1598x^88+28x^89+33x^90+38x^91+40x^92+62x^93+23x^94+1x^176

The gray image is a code over GF(2) with n=704, k=11 and d=328.
This code was found by Heurico 1.16 in 0.922 seconds.