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

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+67x^84+48x^85+117x^86+160x^87+273x^88+744x^89+245x^90+152x^91+133x^92+40x^93+50x^94+8x^95+6x^96+3x^98+1x^174

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 1.22 seconds.