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

generates a code of length 89 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 85.

Homogenous weight enumerator: w(x)=1x^0+68x^85+88x^86+112x^87+180x^88+180x^89+158x^90+96x^91+64x^92+28x^93+8x^94+16x^95+10x^96+12x^97+2x^106+1x^128

The gray image is a code over GF(2) with n=712, k=10 and d=340.
This code was found by Heurico 1.16 in 0.64 seconds.