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

generates a code of length 80 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+191x^74+361x^76+394x^78+325x^80+335x^82+168x^84+140x^86+83x^88+25x^90+13x^92+2x^94+6x^96+1x^98+2x^100+1x^104

The gray image is a code over GF(2) with n=320, k=11 and d=148.
This code was found by Heurico 1.16 in 0.644 seconds.