The generator matrix

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

generates a code of length 78 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+104x^69+337x^70+520x^71+830x^72+978x^73+1129x^74+1176x^75+1245x^76+1532x^77+1351x^78+1192x^79+1234x^80+1132x^81+883x^82+836x^83+635x^84+474x^85+354x^86+168x^87+131x^88+64x^89+38x^90+12x^91+20x^92+2x^93+2x^94+2x^97+2x^98

The gray image is a code over GF(2) with n=312, k=14 and d=138.
This code was found by Heurico 1.16 in 14.4 seconds.