The generator matrix

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

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+161x^72+204x^73+320x^74+208x^75+260x^76+108x^77+190x^78+80x^79+152x^80+64x^81+86x^82+56x^83+38x^84+20x^85+34x^86+8x^87+26x^88+20x^89+10x^90+1x^92+1x^100

The gray image is a code over GF(2) with n=308, k=11 and d=144.
This code was found by Heurico 1.16 in 0.577 seconds.