The generator matrix

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

generates a code of length 77 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+60x^67+382x^68+754x^69+1041x^70+1410x^71+1789x^72+2146x^73+2184x^74+2818x^75+2661x^76+2802x^77+2537x^78+2584x^79+2347x^80+2156x^81+1404x^82+1252x^83+933x^84+654x^85+416x^86+200x^87+131x^88+42x^89+32x^90+10x^91+10x^92+6x^93+2x^95+2x^96+2x^98

The gray image is a code over GF(2) with n=308, k=15 and d=134.
This code was found by Heurico 1.13 in 19.1 seconds.