The generator matrix

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

generates a code of length 82 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+6x^76+242x^77+208x^78+638x^79+156x^80+734x^81+315x^82+652x^83+148x^84+514x^85+156x^86+224x^87+6x^88+42x^89+21x^90+20x^91+2x^92+4x^93+2x^94+2x^95+1x^96+1x^110+1x^134

The gray image is a code over GF(2) with n=656, k=12 and d=304.
This code was found by Heurico 1.16 in 0.64 seconds.