The generator matrix

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

generates a code of length 78 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+96x^67+481x^68+732x^69+1543x^70+1956x^71+2908x^72+3144x^73+4237x^74+4268x^75+5121x^76+5126x^77+5867x^78+5280x^79+5638x^80+4536x^81+4479x^82+2898x^83+2696x^84+1704x^85+1216x^86+666x^87+449x^88+228x^89+126x^90+66x^91+50x^92+14x^93+2x^94+2x^95+4x^97+2x^98

The gray image is a code over GF(2) with n=312, k=16 and d=134.
This code was found by Heurico 1.13 in 75 seconds.