The generator matrix

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

generates a code of length 78 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+106x^72+108x^73+251x^74+180x^75+256x^76+124x^77+231x^78+104x^79+161x^80+116x^81+95x^82+100x^83+91x^84+36x^85+42x^86+10x^88+10x^90+9x^92+9x^94+4x^96+2x^98+2x^100

The gray image is a code over GF(2) with n=312, k=11 and d=144.
This code was found by Heurico 1.16 in 0.565 seconds.