The generator matrix

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

generates a code of length 77 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+68x^66+410x^67+877x^68+1488x^69+2005x^70+2496x^71+3384x^72+4136x^73+4633x^74+4894x^75+5218x^76+5740x^77+5578x^78+5324x^79+5013x^80+4092x^81+3334x^82+2474x^83+1635x^84+1042x^85+717x^86+516x^87+232x^88+130x^89+41x^90+14x^91+22x^92+10x^93+4x^94+2x^96+2x^97+4x^98

The gray image is a code over GF(2) with n=308, k=16 and d=132.
This code was found by Heurico 1.13 in 73.7 seconds.