The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  X  X  X  2  1  0  0  1  2  X  0  X  1  1  X  1  0  2  1  1  0  1  0  2  0  1  1  X  1  2  1  1  1  1  1  1  1  1
 0  X  0  0  0  0  0  0  2  2  X X+2  X  0  0  2 X+2 X+2  X  X  X  X  0  X X+2  X  0  X X+2  2 X+2  2  2 X+2  X  0  0  X  2  2 X+2  2  X  X  2  X  X  X  2  X  X  0  2  2  2  2  X  2  2  X X+2  2  2  2 X+2 X+2  2  X  X  X  0  0  X  2  X  2  0
 0  0  X  0  0  0  0  0  0  0  0  0  2 X+2 X+2 X+2  X X+2 X+2  X  2  2 X+2 X+2  0  0  X  X  X X+2 X+2 X+2  2  2 X+2  X  X  2  2  X  X  0  X  2  X  0  0 X+2 X+2  X  2  0  2  X  2  2  X  2  0  0  X  0  X  X  2 X+2  X  0  2  2 X+2  0 X+2 X+2  2  X  0
 0  0  0  X  0  0  2 X+2  X  X  X  X  2 X+2  X  2  2  0  2  2  2  2  2  X X+2  X  2  X X+2 X+2  X X+2  0  2  0  0  0 X+2  2  X X+2  0  0  0  X  X  2  X  2  X X+2  2 X+2 X+2  0  X X+2  0  2 X+2  2  X  0  2  2 X+2  2  2  X  0  2  0  2  X  0  X  0
 0  0  0  0  X  0 X+2 X+2  X  2 X+2 X+2  0  X  X  0  2  X  0 X+2 X+2  X X+2  X  2  2  X  2  2  0 X+2  2  0 X+2  X X+2  2  0  X  0  0  2  0  X  0  X  2  0  2  X X+2  0  0 X+2  X X+2  0  2  X  2  2  0 X+2 X+2  2  2  0  2  X  2  2 X+2  0  2  2  X  0
 0  0  0  0  0  X  X  2 X+2  X X+2  2  X  X  0  X  0 X+2 X+2  0  X  2  2 X+2  2  X X+2 X+2  2  X  2  2 X+2  0  X X+2  0  0  X  X  0 X+2  2  2  2 X+2 X+2  X X+2  X X+2  0  0  0 X+2  2  0  X  X  0 X+2  2  0  2  2  2  X  X  2  0 X+2  0  2 X+2  2  0  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+34x^66+90x^67+164x^68+198x^69+261x^70+332x^71+393x^72+386x^73+530x^74+708x^75+702x^76+784x^77+728x^78+598x^79+487x^80+472x^81+352x^82+226x^83+220x^84+150x^85+91x^86+68x^87+67x^88+46x^89+42x^90+24x^91+10x^92+12x^93+8x^94+2x^95+4x^96+1x^98+1x^114

The gray image is a code over GF(2) with n=308, k=13 and d=132.
This code was found by Heurico 1.16 in 6.92 seconds.