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

generates a code of length 88 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 85.

Homogenous weight enumerator: w(x)=1x^0+114x^85+198x^86+122x^87+208x^88+134x^89+123x^90+62x^91+22x^92+16x^93+10x^94+9x^96+4x^98+1x^130

The gray image is a code over GF(2) with n=704, k=10 and d=340.
This code was found by Heurico 1.16 in 0.516 seconds.