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

generates a code of length 89 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+154x^84+32x^86+621x^88+512x^89+480x^90+184x^92+57x^96+6x^100+1x^168

The gray image is a code over GF(2) with n=712, k=11 and d=336.
This code was found by Heurico 1.16 in 3.44 seconds.