The generator matrix

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

generates a code of length 77 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 65.

Homogenous weight enumerator: w(x)=1x^0+128x^65+565x^66+1058x^67+1603x^68+2582x^69+3691x^70+4658x^71+6263x^72+7876x^73+9318x^74+10368x^75+11273x^76+11636x^77+11307x^78+11118x^79+9439x^80+8012x^81+6552x^82+4708x^83+3463x^84+2204x^85+1358x^86+860x^87+525x^88+238x^89+125x^90+58x^91+33x^92+26x^93+12x^94+4x^95+8x^96+2x^97

The gray image is a code over GF(2) with n=308, k=17 and d=130.
This code was found by Heurico 1.13 in 268 seconds.