The generator matrix

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

generates a code of length 79 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+119x^74+158x^76+537x^78+512x^79+516x^80+80x^82+55x^84+46x^86+3x^88+13x^90+2x^92+5x^94+1x^140

The gray image is a code over GF(2) with n=632, k=11 and d=296.
This code was found by Heurico 1.16 in 10.7 seconds.