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

generates a code of length 78 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 73.

Homogenous weight enumerator: w(x)=1x^0+204x^73+213x^74+268x^75+150x^76+244x^77+165x^78+234x^79+87x^80+112x^81+83x^82+114x^83+14x^84+60x^85+12x^86+22x^87+16x^88+12x^89+11x^90+2x^91+4x^92+11x^94+8x^97+1x^98

The gray image is a code over GF(2) with n=312, k=11 and d=146.
This code was found by Heurico 1.16 in 14 seconds.