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

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

Homogenous weight enumerator: w(x)=1x^0+51x^82+142x^84+114x^86+512x^87+427x^88+512x^89+108x^90+122x^92+38x^94+11x^96+9x^98+1x^168

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.