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

generates a code of length 76 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 65.

Homogenous weight enumerator: w(x)=1x^0+96x^65+429x^66+912x^67+1263x^68+2176x^69+2333x^70+3386x^71+3618x^72+4922x^73+4895x^74+5968x^75+5396x^76+5946x^77+5216x^78+4938x^79+3834x^80+3572x^81+2129x^82+1792x^83+1091x^84+750x^85+403x^86+258x^87+86x^88+64x^89+19x^90+24x^91+2x^92+8x^93+2x^95+5x^96+2x^97

The gray image is a code over GF(2) with n=304, k=16 and d=130.
This code was found by Heurico 1.13 in 72.5 seconds.