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

generates a code of length 89 over Z4[X]/(X^2+2) who�s minimum homogenous weight is 83.

Homogenous weight enumerator: w(x)=1x^0+112x^83+147x^84+234x^85+407x^86+376x^87+644x^88+458x^89+559x^90+418x^91+265x^92+146x^93+111x^94+104x^95+25x^96+30x^97+10x^98+30x^99+6x^100+8x^101+4x^105+1x^154

The gray image is a code over GF(2) with n=712, k=12 and d=332.
This code was found by Heurico 1.16 in 1.19 seconds.