The generator matrix

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

generates a code of length 79 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 73.

Homogenous weight enumerator: w(x)=1x^0+130x^73+199x^74+152x^75+160x^76+168x^77+177x^78+150x^79+145x^80+162x^81+171x^82+134x^83+139x^84+110x^85+11x^86+2x^87+1x^88+4x^89+10x^90+10x^91+1x^92+2x^93+6x^94+1x^96+2x^110

The gray image is a code over GF(2) with n=316, k=11 and d=146.
This code was found by Heurico 1.16 in 55.4 seconds.