The generator matrix

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

generates a code of length 88 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+66x^78+638x^79+1856x^80+4124x^81+6751x^82+10802x^83+15922x^84+20046x^85+25778x^86+28744x^87+31367x^88+29626x^89+27119x^90+21002x^91+15416x^92+9970x^93+6276x^94+3458x^95+1534x^96+880x^97+420x^98+190x^99+80x^100+36x^101+14x^102+8x^103+6x^105+4x^106+6x^107+4x^110

The gray image is a code over GF(2) with n=704, k=18 and d=312.
This code was found by Heurico 1.16 in 829 seconds.