The generator matrix

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

generates a code of length 78 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 71.

Homogenous weight enumerator: w(x)=1x^0+66x^71+792x^72+1258x^73+2345x^74+3000x^75+3508x^76+3646x^77+4142x^78+3674x^79+3472x^80+2636x^81+1916x^82+924x^83+704x^84+294x^85+215x^86+90x^87+25x^88+22x^89+21x^90+4x^91+6x^92+1x^94+2x^95+4x^96

The gray image is a code over GF(2) with n=624, k=15 and d=284.
This code was found by Heurico 1.16 in 12.9 seconds.