The generator matrix

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

generates a code of length 77 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+44x^72+136x^73+129x^74+122x^75+94x^76+78x^77+114x^78+74x^79+66x^80+38x^81+30x^82+38x^83+18x^84+14x^85+11x^86+6x^87+2x^89+1x^90+4x^93+2x^94+1x^96+1x^102

The gray image is a code over GF(2) with n=308, k=10 and d=144.
This code was found by Heurico 1.16 in 0.283 seconds.