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

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+64x^85+76x^86+184x^87+46x^88+292x^89+88x^90+180x^91+8x^92+24x^93+28x^94+16x^95+6x^96+4x^97+4x^99+2x^104+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 0.844 seconds.