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  X  1  X  1  X  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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  1  1  2  X
 0 2X+2  0  0  0  2 2X+2  2  0  0  0  0  2 2X+2  2 2X+2  0  0  0  0  2 2X+2  2 2X+2  0  0  2 2X+2 2X  0 2X  2 2X  0 2X 2X+2 2X 2X+2 2X  2 2X 2X+2 2X  2 2X 2X+2 2X  2  2 2X 2X 2X+2 2X+2 2X  2 2X 2X 2X  2 2X+2 2X+2  2 2X 2X 2X 2X 2X+2  2  0 2X  2 2X+2  0  2 2X 2X+2 2X  2 2X 2X+2 2X 2X 2X+2 2X+2 2X+2  2  0  0
 0  0 2X+2  0  2  2 2X+2  0  0  0  2 2X+2  2 2X+2  0  0 2X 2X 2X+2  2 2X+2  2 2X 2X 2X 2X 2X+2  2 2X 2X+2  2 2X  0  2 2X+2 2X 2X 2X+2  0 2X+2 2X+2 2X 2X+2  0 2X 2X+2 2X+2 2X  2 2X  2 2X  2  0 2X  2  0 2X+2 2X+2  0  2  2  0 2X  2  2  0  0  0 2X+2  2 2X  0 2X+2 2X+2  0 2X  0  2 2X  0  0 2X+2 2X  2  0 2X+2  0
 0  0  0 2X+2  2  0 2X+2  2 2X  2 2X+2 2X 2X  2 2X+2 2X 2X  2 2X+2 2X 2X  2 2X+2 2X  0 2X+2  0 2X+2 2X+2  2  0  2  2  0 2X  0  0  0  2  2  2  2 2X 2X 2X 2X  0  0  2 2X+2 2X+2 2X+2 2X 2X 2X  0 2X+2 2X+2 2X+2 2X+2  0 2X+2  0  2  2 2X  2  0  0  2  0 2X+2 2X  0 2X+2 2X+2  0 2X+2  0 2X  2 2X  2 2X 2X+2  0 2X  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+63x^84+4x^85+84x^86+188x^87+364x^88+188x^89+64x^90+4x^91+44x^92+12x^94+6x^96+1x^100+1x^160

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 0.609 seconds.