The generator matrix

 1  0  1  1  1  0  1  1  0  1  2  1  1  1 X+2  1  X  1  1  1  X  1  2  1  1  X  1  1  X  1  1  X  1  1  1  1  X  0  1  X  1  1  1 X+2  1  1  1  1 X+2  1 X+2  0  1  X  0  1  1  1  0  X  1  1  2  0  1  1 X+2  1  X  1  1 X+2 X+2  X  X  X  1
 0  1  1  0  1  1  2 X+1  1  0  1  3 X+3  0  1  1  1  2  2 X+1  1 X+2  1 X+1  1  1  0  0  1 X+3 X+1  1  2 X+1  2 X+3  1  1 X+2  1  X X+1 X+2  1  1 X+2 X+3  0  1 X+1  1  1 X+3  1  1  2  1  X  X  1  2 X+1  1  1  1  1  1 X+2  1 X+1  X  1  1  2 X+2  0  2
 0  0  X  0  0  0  0  0  0  0  0  0  2  X X+2 X+2 X+2 X+2 X+2  X  X  X X+2  2 X+2  0  X X+2  2  2 X+2  2  X  0  2  X X+2  X  X X+2  2  0  X  0  X  2 X+2  2 X+2  2  0 X+2  2  X  X  0  X  0  0  0  X  X  2  2  X X+2  2 X+2  X X+2 X+2  0  X  0  0  0  0
 0  0  0  X  0  0  0  0  X X+2 X+2  X X+2 X+2 X+2 X+2  0 X+2  2  2 X+2  2  0 X+2 X+2 X+2  X  X X+2  X  2  0  2  2  X X+2  0 X+2  X  2  X X+2  0  2  X  0  X  0  0 X+2 X+2  0 X+2  2  X  2  2  X  0  0  X  X X+2 X+2  0 X+2 X+2  2  2 X+2  0  X  0  X  X  2  0
 0  0  0  0  X  0  2 X+2  0  2  0 X+2  X  X  X  2  X X+2  X  0  X X+2 X+2  X  2 X+2  2  0 X+2  0 X+2  X  0  2 X+2 X+2  0  0  0  0  2  0  2  0 X+2 X+2 X+2  0  2  0  2  X  X  2  X  2  2 X+2  X X+2  X  2  2 X+2  0  0  0 X+2 X+2  2  2 X+2  2  X  X  2  0
 0  0  0  0  0  X X+2 X+2 X+2 X+2  2  2  X X+2 X+2  2  2  0 X+2 X+2  0  0 X+2  2 X+2 X+2  2 X+2  0  2  X  0  2  2  0  0  X  0 X+2  0  X X+2  X  0  0  2  X  2  X  0 X+2  2 X+2  0  0 X+2  2 X+2 X+2 X+2  X  0  0 X+2  2 X+2 X+2  2  2  X  0  0  0 X+2 X+2  2 X+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+37x^66+108x^67+212x^68+366x^69+494x^70+562x^71+793x^72+1036x^73+1192x^74+1282x^75+1455x^76+1558x^77+1373x^78+1274x^79+1137x^80+1024x^81+769x^82+554x^83+424x^84+246x^85+180x^86+92x^87+59x^88+44x^89+34x^90+24x^91+11x^92+14x^93+17x^94+8x^95+2x^96+2x^100

The gray image is a code over GF(2) with n=308, k=14 and d=132.
This code was found by Heurico 1.16 in 17.9 seconds.