The generator matrix

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

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+76x^73+212x^74+152x^75+250x^76+134x^77+249x^78+124x^79+209x^80+94x^81+127x^82+96x^83+140x^84+38x^85+43x^86+22x^87+30x^88+22x^89+6x^90+4x^91+7x^92+4x^93+2x^94+2x^95+2x^96+1x^100+1x^114

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 0.587 seconds.