The generator matrix

 1  0  0  1  1  1 X+2  X  1  1  X  1  1  2  1  1 X+2  1  0  X  1  1  1  X  1  2  0  1  1  1  1  1  1  1  2  0  1  1  0 X+2  1  1  1  X  1  1  1 X+2  2  X  1  1 X+2  1  1  1  1  1  0  1  X  0  1  1  1  2  1 X+2  0  2  X X+2  1  X  1 X+2  X
 0  1  0  0  3 X+1  1  2  2 X+3  1  2  1  1  0  3  1 X+1  1  2 X+2  2  1  1 X+3  1  0  X  X  0 X+2  2  2  2  2  2 X+2  X  1  1  3  1  2  1  1  0 X+2  1  1  1  0 X+2  0 X+1 X+1 X+1  X  3 X+2 X+3  X  1  X  1  0  X  X  1  1  0  X  X  1  0  X  1 X+2
 0  0  1  1  3  2  3  1  0 X+1  0 X+3  2  1  2  1  1  0  2  1  3  2  0  2 X+3  3  1 X+3  1 X+3 X+1 X+2 X+2  1  1  1  1  1  X X+1  X X+1  3 X+1  1 X+2 X+1  X X+3 X+2 X+3 X+3  1  2  X  1  X X+2  1 X+3  1 X+1  X  0 X+1  0  3  3 X+3  2  2  1  X X+2  X  2  2
 0  0  0  X  X  0  X  X  X  0  X  0  X  0  2 X+2 X+2  2  2 X+2 X+2 X+2 X+2 X+2  2  2  2  0  0 X+2 X+2  X X+2  2 X+2  X  2  X X+2  2  0  0  0 X+2  0  0  2  X X+2  0  X  X  2 X+2  0 X+2  2  2 X+2 X+2  0  0  X  2 X+2  X  2  2  X  X  X  0  2  X  2  2  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+344x^72+382x^74+488x^76+228x^78+303x^80+124x^82+102x^84+20x^86+28x^88+14x^90+2x^92+4x^96+8x^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 11.4 seconds.